In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is als...In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.展开更多
Understanding the mechanisms of community assembly is a key question in ecology.Metal pollution may result in significant changes in bird community structure and diversity,with implications for ecosystem processes and...Understanding the mechanisms of community assembly is a key question in ecology.Metal pollution may result in significant changes in bird community structure and diversity,with implications for ecosystem processes and function.However,the relative importance of these pro-cesses in shaping the bird community at the polluted area is still not clear.Here,we explored bird species richness,functional,and phylogenetic diversity,and the assembly processes of community at the mine region of southwest China.Our results showed that the 3 dimensions of diversity at the mine area were lower than that at the reference sites.In the community assembly,the result was O<NRI/NFR1<1.96,which indicated deterministic processes(environmental filtering)might drive community clustering.The results of the neutral community model,and normalized stochasticity ratio,showed the dominant role of stochastic processes in shaping the bird community assembly.We further quanti-fied the community-level habitat niche breadth(Bcom),and we found that there was no difference in Bcom-value between the mine area and reference sites.This indicates that the bird communities at the mine area and 3 reference sites were not subjected to extreme environmental selection(same or different resource allocation)to form a highly specialized niche.These findings provide insights into the distribution patterns and dominant ecological processes of bird communities under metal exposure,and extend the knowledge in community assembly mechanisms of bird communities living in the mine area.展开更多
In this article, we summarize some results on invariant non-homogeneous and dynamic-equilibrium (DE) continuous Markov stochastic processes. Moreover, we discuss a few examples and consider a new application of DE pro...In this article, we summarize some results on invariant non-homogeneous and dynamic-equilibrium (DE) continuous Markov stochastic processes. Moreover, we discuss a few examples and consider a new application of DE processes to elements of survival analysis. These elements concern the stochastic quadratic-hazard-rate model, for which our work 1) generalizes the reading of its It? stochastic ordinary differential equation (ISODE) for the hazard-rate-driving independent (HRDI) variables, 2) specifies key properties of the hazard-rate function, and in particular, reveals that the baseline value of the HRDI variables is the expectation of the DE solution of the ISODE, 3) suggests practical settings for obtaining multi-dimensional probability densities necessary for consistent and systematic reconstruction of missing data by Gibbs sampling and 4) further develops the corresponding line of modeling. The resulting advantages are emphasized in connection with the framework of clinical trials of chronic obstructive pulmonary disease (COPD) where we propose the use of an endpoint reflecting the narrowing of airways. This endpoint is based on a fairly compact geometric model that quantifies the course of the obstruction, shows how it is associated with the hazard rate, and clarifies why it is life-threatening. The work also suggests a few directions for future research.展开更多
This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process mode...This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.展开更多
Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics ...Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation [J. Chem. Phys. 147, 184104 （2017）] in principle exists in other types of stochastic thermostats as well. The recommended ＂middle＂ scheme [J. Chem. Phys. 147, 034109 （2017）] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation thermostatting processes with molecular is proposed for understanding efficient stochastic dynamics.展开更多
In order to improve the influence of the uncertain and dynamic of node enterprise behavior on the performance of supply chain,the method based on stochastic process algebra for description,analysis,validation and eval...In order to improve the influence of the uncertain and dynamic of node enterprise behavior on the performance of supply chain,the method based on stochastic process algebra for description,analysis,validation and evaluation of supply chain business process model is proposed.Firstly,the description of the uncertainty of node enterprise behavior is given using the extended Unified Modeling Language sequence diagram,and mapping rule is defined from the extended Unified Modeling Language sequence diagram to stochastic process algebra.Secondly,on the basis of the acquired stochastic process algebra model,the supply chain business process model is verified with Mobility Workbench.Finally,according to the operational semantics of stochastic process algebra,the continuous-time Markov chain,isomorphic with stochastic process algebra model,is built; and the system performance evaluation of transient status and stable status is respectively conducted in accordance with Markov transfer relations and the current state of system,obtaining the predicted performance value and average performance index value for a specific period of time.The simulation experiments show that the proposed method can accurately describe the stochastic behaviors of supply chain system and interactions among nodes,effectively verify the validity of the model,and objectively and exactly evaluate design of the supply chain.展开更多
This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning...This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.展开更多
The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requireme...The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.展开更多
This paper contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. Identifi...This paper contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. Identification development follows a transparent image processing paradigm completely independent of state-of-the-art structural dynamics, aiming at delivering a simple and wide purpose method. Validation of the proposed importance sampling strategy is based on multi-scale clusters of realizations of digitally generated non-stationary stochastic processes. Good agreement with the reference pure Monte Carlo results indicates a significant potential in reducing the computational task of first passage probabilities estimation, an important feature in the field of e.g., probabilistic seismic design or risk assessment generally.展开更多
This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construct...This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construction methods extends its applicability to diverse stochastic processes also including discrete as well as continuous time cases.The initially given two arbitrary univariate stochastic processes{Y_(t)},{Z_(t)},are only assumed to share the same time t.When considered as describing(time dependent)random quantities that are physically separated(the baseline case),the processes are independent.From this trivial case we move to the case when physical interactions between the quantities make them stochastically dependent random variables at any moment t.For each time epoch t,we impose stochastic dependence on two“initially independent”random variables Y_(t),Z_(t) by multiplying the product of their survival functions by a proper“dependence factor”φ_(t)(y_(t), z_(t)),obtaining in this way a universal(“canonical”)form valid for any(!)bivariate distribution.In some known cases,however,this form may become complicated thou it always exists and is unique.The dependence factor,basically,but not always,has the form φ_(t)(y, z)=exp[-∫^(y)_(0)∫^(z)_(0)Ψ_(t)(s ,u )dsdu]whenever such a continuous function Ψ_(t)(s ,u ) exists,for each t.That representation of stochastic dependence by the functions Ψ_(t)(s ,u ) leads,in turn,to the phenomenon of change of the original(baseline)hazard rates of the marginals,similar to those analyzed by Cox and,especially Aalen for single pairs(or sets)of,time independent,random variables.That is why,until Section 4,we consider only single random vectors(Y,Z)'joint survival functions,mostly as a preparation to the theory of bivariate stochastic processes{(Y_(t),Z_(t))}constructions as initiated in Section 4.The bivariate constructions are illustrated by examples of some applications in biomedical and econometric areas.展开更多
Anthropogenic environmental changes may affect community assembly through mediating both deterministic(e.g.,competitive exclusion and environmental filtering)and stochastic processes(e.g.,birth/death and dispersal/col...Anthropogenic environmental changes may affect community assembly through mediating both deterministic(e.g.,competitive exclusion and environmental filtering)and stochastic processes(e.g.,birth/death and dispersal/colonization).It is traditionally thought that environmental changes have a larger mediation effect on stochastic processes in structuring soil microbial community than aboveground plant community;however,this hypothesis remains largely untested.Here we report an unexpected pattern that nitrogen(N)deposition has a larger mediation effect on stochastic processes in structuring plant community than soil microbial community(those<2 mm in diameter,including archaea,bacteria,fungi,and protists)in the Eurasian steppe.We performed a ten-year nitrogen deposition experiment in a semiarid grassland ecosystem in Inner Mongolia,manipulating nine rates(0–50 g N m^(-2)per year)at two frequencies(nitrogen added twice or 12 times per year)under two grassland management strategies(fencing or mowing).We separated the compositional variation of plant and soil microbial communities caused by each treatment into the deterministic and stochastic components with a recently-developed method.As nitrogen addition rate increased,the relative importance of stochastic component of plant community first increased and then decreased,while that of soil microbial community first decreased and then increased.On the whole,the relative importance of stochastic component was significantly larger in plant community(0.552±0.035;mean±standard error)than in microbial community(0.427±0.035).Consistently,the proportion of compositional variation explained by the deterministic soil and community indices was smaller for plant community(0.172–0.186)than microbial community(0.240–0.767).Meanwhile,as nitrogen addition rate increased,the linkage between plant and microbial community composition first became weaker and then became stronger.The larger stochasticity in plant community relative to microbial community assembly suggested that more stochastic strategies(e.g.,seeds addition)should be adopted to maintain above-than below-ground biodiversity under the pressure of nitrogen deposition.展开更多
Photovoltaic (PV) modules, as essential components of solar power generation systems, significantly influence unitpower generation costs.The service life of these modules directly affects these costs. Over time, the p...Photovoltaic (PV) modules, as essential components of solar power generation systems, significantly influence unitpower generation costs.The service life of these modules directly affects these costs. Over time, the performanceof PV modules gradually declines due to internal degradation and external environmental factors.This cumulativedegradation impacts the overall reliability of photovoltaic power generation. This study addresses the complexdegradation process of PV modules by developing a two-stage Wiener process model. This approach accountsfor the distinct phases of degradation resulting from module aging and environmental influences. A powerdegradation model based on the two-stage Wiener process is constructed to describe individual differences inmodule degradation processes. To estimate the model parameters, a combination of the Expectation-Maximization(EM) algorithm and the Bayesian method is employed. Furthermore, the Schwarz Information Criterion (SIC) isutilized to identify critical change points in PV module degradation trajectories. To validate the universality andeffectiveness of the proposed method, a comparative analysis is conducted against other established life predictiontechniques for PV modules.展开更多
Laboratory experiments are one of the important means used to investigate travel choice behavior under strategic uncertainty.Many experiment-based studies have shown that the Nash equilibrium can predict aggregated ro...Laboratory experiments are one of the important means used to investigate travel choice behavior under strategic uncertainty.Many experiment-based studies have shown that the Nash equilibrium can predict aggregated route choices,while the fluctuations,whose mechanisms are still unclear,continue to exist until the end.To understand the fluctuations,this paper proposes a route-dependent attraction-based stochastic process model,which shares exactly the same behavioral foundation introduced in Part I of the study(Qi et al.,2023),i.e.,route-dependent inertia and route-dependent preference.The model predictions are carefully compared with the experimental observations obtained from the congestible parallel-route laboratory experiments containing 312 subjects and eight decision-making scenarios(Qi et al.,2023).The results show that the proposed stochastic process model can precisely reproduce the random oscillations both in terms of flow switching and route flow evolution.Subsequently,an approximated model is developed to enhance the efficiency in evaluating the equilibrium distribution,providing a practical tool to evaluate the impacts of transportation policies in both long-and short-term runs.To the best of our knowledge,this paper is the first attempt to model and explain experimental phenomena by introducing stochastic process theories,as well as a successful example of applying experimental economics methodology to improve our understanding of human travel choice behavior.展开更多
Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of ...Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of different soil microbial taxa under environmental changes are still disputed,which limits the understanding of the sustainability of desert restoration.Hence,we investigated the soil microbial community characteristics and functional attributes of grassland desert(GD),desert steppe(DS),typical steppe(TS),and artificial forest(AF)in the Mu Us Desert,China.Our findings confirmed the geographical conservation of soil microbial composition but highlighted decreased microbial diversity in TS.Meanwhile,the abundance of rare taxa and microbial community stability in TS improved.Heterogeneous and homogeneous selection determined the assembly of rare and abundant bacterial taxa,respectively,with both being significantly influenced by soil moisture.In contrast,fungal communities displayed stochastic processes and exhibited sensitivity to soil nutrient conditions.Furthermore,our investigation revealed a noteworthy augmentation in bacterial metabolic functionality in TS,aligning with improved vegetation restoration and the assemblage of abundant bacterial taxa.However,within nutrient-limited soils(GD,DS,and AF),the assembly dynamics of rare fungal taxa assumed a prominent role in augmenting their metabolic capacity and adaptability to desert ecosystems.These results highlighted the variations in the assembly processes and metabolic functions of soil microorganisms during vegetation reestablishment and provided corresponding theoretical support for anthropogenic revegetation of desert ecosystems.展开更多
Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area unde...Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area under random resource competition and is based on two assumptions:(1)a sigmoid-type stochastic process governs tree and stand basal area dynamics of living and dying trees,and(2)the total area that a tree may potentially occupy determines the number of trees per hectare.The most effective method to satisfy these requirements is formalizing each tree diameter and potentially occupied area using Gompertz-type stochastic differential equations governed by fixed and mixed-effect parameters.Data from permanent experimental plots from long-term Lithuania experiments were used to construct the tree and stand basal area models.The new models were relatively unbiased for live trees of all species,including silver birch(Betula pen-dula Roth)and downy birch(Betula pubescens Ehrh.),[spruce(Picea abies),and pine(Pinus sylvestris)].Less reliable predic-tions were made for the basal area of dying trees.Pines gave the highest accuracy prediction of mean basal area among all live trees.The mean basal area prediction for all dying trees was lower than that for live trees.Among all species,pine also had the best average basal area prediction accuracy for live trees.Newly developed basal area growth and yield models can be recommended despite their complex formulation and implementation challenges,particularly in situations when data is scarce.This is because the newly observed plot provides sufficient information to calibrate random effects.展开更多
We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
With the increasing penetration of renewable energy resources(RESs), the uncertainties of volatile renewable generations significantly affect the power system operation. Such uncertainties are usually modeled as stoch...With the increasing penetration of renewable energy resources(RESs), the uncertainties of volatile renewable generations significantly affect the power system operation. Such uncertainties are usually modeled as stochastic variables obeying specific distributions by neglecting the temporal correlations. Conventional approaches to hedge the negative effects caused by such uncertainties are thus hard to pursue a trade-off between computation efficiency and optimality. As an alternative, the theory of stochastic process can naturally model temporal correlation in closed forms. Attracted by this feature, our research group has been conducting thorough researches in the past decade to introduce stochastic processes within renewable power systems. This paper summarizes our works from the perspective of both the frequency domain and the time domain, provides the tools for the analysis and control of power systems under a unified framework of stochastic processes, and discusses the underlying reasons that stochastic process-based approaches can perform better than conventional approaches on both computational efficiency and optimality. These work may shed a new light on the research of analysis, control and operation of renewable power systems.Finally, this paper outlooks the theoretic developments of stochastic processes in future’s renewable power systems.展开更多
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. A formal analysis method of survivable network was proposed based on stochastic process algebra, which i...Stochastic process algebras have been proposed as compositional specification formalisms for performance models. A formal analysis method of survivable network was proposed based on stochastic process algebra, which incorporates formal modeling into performance analysis perfectly, and then various performance parameters of survivable network can be simultaneously obtained after formal modeling. The formal description with process expression to the survivable network system was carried out based on the simply introduced syntax and operational semantics of stochastic process algebra. Then PEPA workbench tool was used to obtain the probability of system’s steady state availability and transient state availability. Simulation experiments show the effectiveness and feasibility of the developed method.展开更多
Nematodes play an important role in ecosystems;however,very little is known about their assembly processes and the factors influencing them.We studied nematode communities in bulk soils from three Asian mountain ecosy...Nematodes play an important role in ecosystems;however,very little is known about their assembly processes and the factors influencing them.We studied nematode communities in bulk soils from three Asian mountain ecosystems to determine the assembly processes of free-living nematode metacommunities and their driving factors.On each mountain,elevations span a range of climatic conditions with the potential to reveal assembly processes that predominate across multiple biomes.A phylogenetic null modeling framework was used to analyze 18S rRNA gene amplicons to quantify various assembly processes.We found that phylogenetic turnover between nematode communities on all mountains was dominated by stochastic processes,with“undominated processes”being the most predominant stochastic factor.Elevation has a significant impact on the relative importance of deterministic and stochastic processes.A variety of climatic and edaphic variables significantly influenced the variations in community assembly processes with elevation,even though their impacts were not consistent between the mountains.Overall,our results indicate that free-living nematode metacommunities in a wide range of environments are largely structured by stochastic processes rather than by niche-based deterministic processes,suggesting that metacommunities of soil free-living nematodes may respond to climate change in a largely unpredictable way.展开更多
The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set value...The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set valued stochastic processes are obtained.展开更多
基金Supported by the National Natural Science Foundation of China(12171247)。
文摘In this short paper, we first establish the existence of periodic solutions to parabolic equation in the whole space by using the probability method. Then, the periodicity of some function of stochastic process is also studied.
文摘Understanding the mechanisms of community assembly is a key question in ecology.Metal pollution may result in significant changes in bird community structure and diversity,with implications for ecosystem processes and function.However,the relative importance of these pro-cesses in shaping the bird community at the polluted area is still not clear.Here,we explored bird species richness,functional,and phylogenetic diversity,and the assembly processes of community at the mine region of southwest China.Our results showed that the 3 dimensions of diversity at the mine area were lower than that at the reference sites.In the community assembly,the result was O<NRI/NFR1<1.96,which indicated deterministic processes(environmental filtering)might drive community clustering.The results of the neutral community model,and normalized stochasticity ratio,showed the dominant role of stochastic processes in shaping the bird community assembly.We further quanti-fied the community-level habitat niche breadth(Bcom),and we found that there was no difference in Bcom-value between the mine area and reference sites.This indicates that the bird communities at the mine area and 3 reference sites were not subjected to extreme environmental selection(same or different resource allocation)to form a highly specialized niche.These findings provide insights into the distribution patterns and dominant ecological processes of bird communities under metal exposure,and extend the knowledge in community assembly mechanisms of bird communities living in the mine area.
文摘In this article, we summarize some results on invariant non-homogeneous and dynamic-equilibrium (DE) continuous Markov stochastic processes. Moreover, we discuss a few examples and consider a new application of DE processes to elements of survival analysis. These elements concern the stochastic quadratic-hazard-rate model, for which our work 1) generalizes the reading of its It? stochastic ordinary differential equation (ISODE) for the hazard-rate-driving independent (HRDI) variables, 2) specifies key properties of the hazard-rate function, and in particular, reveals that the baseline value of the HRDI variables is the expectation of the DE solution of the ISODE, 3) suggests practical settings for obtaining multi-dimensional probability densities necessary for consistent and systematic reconstruction of missing data by Gibbs sampling and 4) further develops the corresponding line of modeling. The resulting advantages are emphasized in connection with the framework of clinical trials of chronic obstructive pulmonary disease (COPD) where we propose the use of an endpoint reflecting the narrowing of airways. This endpoint is based on a fairly compact geometric model that quantifies the course of the obstruction, shows how it is associated with the hazard rate, and clarifies why it is life-threatening. The work also suggests a few directions for future research.
基金supported by the Science Challenge Project,China(No.TZ2018007)the National Science Fund for Distinguished Young Scholars,China(No.51725502)+2 种基金the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.51621004)the Fundamental Research Foundation of China(No.JCKY2020110C105)the National Natural Science Foundation of China(No.52105253)。
文摘This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.
文摘Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation [J. Chem. Phys. 147, 184104 （2017）] in principle exists in other types of stochastic thermostats as well. The recommended ＂middle＂ scheme [J. Chem. Phys. 147, 034109 （2017）] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation thermostatting processes with molecular is proposed for understanding efficient stochastic dynamics.
基金Sponsored by the National High-Tech.R&D Program for CIMS,China(Grant No.2007AA04Z146)
文摘In order to improve the influence of the uncertain and dynamic of node enterprise behavior on the performance of supply chain,the method based on stochastic process algebra for description,analysis,validation and evaluation of supply chain business process model is proposed.Firstly,the description of the uncertainty of node enterprise behavior is given using the extended Unified Modeling Language sequence diagram,and mapping rule is defined from the extended Unified Modeling Language sequence diagram to stochastic process algebra.Secondly,on the basis of the acquired stochastic process algebra model,the supply chain business process model is verified with Mobility Workbench.Finally,according to the operational semantics of stochastic process algebra,the continuous-time Markov chain,isomorphic with stochastic process algebra model,is built; and the system performance evaluation of transient status and stable status is respectively conducted in accordance with Markov transfer relations and the current state of system,obtaining the predicted performance value and average performance index value for a specific period of time.The simulation experiments show that the proposed method can accurately describe the stochastic behaviors of supply chain system and interactions among nodes,effectively verify the validity of the model,and objectively and exactly evaluate design of the supply chain.
文摘This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.
文摘The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.
文摘This paper contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. Identification development follows a transparent image processing paradigm completely independent of state-of-the-art structural dynamics, aiming at delivering a simple and wide purpose method. Validation of the proposed importance sampling strategy is based on multi-scale clusters of realizations of digitally generated non-stationary stochastic processes. Good agreement with the reference pure Monte Carlo results indicates a significant potential in reducing the computational task of first passage probabilities estimation, an important feature in the field of e.g., probabilistic seismic design or risk assessment generally.
文摘This paper proposes a universal framework for constructing bivariate stochastic processes,going beyond the limitations of copulas and offering a potentially simpler alternative.The achieved generality of the construction methods extends its applicability to diverse stochastic processes also including discrete as well as continuous time cases.The initially given two arbitrary univariate stochastic processes{Y_(t)},{Z_(t)},are only assumed to share the same time t.When considered as describing(time dependent)random quantities that are physically separated(the baseline case),the processes are independent.From this trivial case we move to the case when physical interactions between the quantities make them stochastically dependent random variables at any moment t.For each time epoch t,we impose stochastic dependence on two“initially independent”random variables Y_(t),Z_(t) by multiplying the product of their survival functions by a proper“dependence factor”φ_(t)(y_(t), z_(t)),obtaining in this way a universal(“canonical”)form valid for any(!)bivariate distribution.In some known cases,however,this form may become complicated thou it always exists and is unique.The dependence factor,basically,but not always,has the form φ_(t)(y, z)=exp[-∫^(y)_(0)∫^(z)_(0)Ψ_(t)(s ,u )dsdu]whenever such a continuous function Ψ_(t)(s ,u ) exists,for each t.That representation of stochastic dependence by the functions Ψ_(t)(s ,u ) leads,in turn,to the phenomenon of change of the original(baseline)hazard rates of the marginals,similar to those analyzed by Cox and,especially Aalen for single pairs(or sets)of,time independent,random variables.That is why,until Section 4,we consider only single random vectors(Y,Z)'joint survival functions,mostly as a preparation to the theory of bivariate stochastic processes{(Y_(t),Z_(t))}constructions as initiated in Section 4.The bivariate constructions are illustrated by examples of some applications in biomedical and econometric areas.
基金supported by the National Natural Science Foundation of China(32071547,U21A20188)the Top-Notch Young Talents Program(to Ximei Zhang)of Chinathe Agricultural Science and Technology Innovation Program(to Ximei Zhang)。
文摘Anthropogenic environmental changes may affect community assembly through mediating both deterministic(e.g.,competitive exclusion and environmental filtering)and stochastic processes(e.g.,birth/death and dispersal/colonization).It is traditionally thought that environmental changes have a larger mediation effect on stochastic processes in structuring soil microbial community than aboveground plant community;however,this hypothesis remains largely untested.Here we report an unexpected pattern that nitrogen(N)deposition has a larger mediation effect on stochastic processes in structuring plant community than soil microbial community(those<2 mm in diameter,including archaea,bacteria,fungi,and protists)in the Eurasian steppe.We performed a ten-year nitrogen deposition experiment in a semiarid grassland ecosystem in Inner Mongolia,manipulating nine rates(0–50 g N m^(-2)per year)at two frequencies(nitrogen added twice or 12 times per year)under two grassland management strategies(fencing or mowing).We separated the compositional variation of plant and soil microbial communities caused by each treatment into the deterministic and stochastic components with a recently-developed method.As nitrogen addition rate increased,the relative importance of stochastic component of plant community first increased and then decreased,while that of soil microbial community first decreased and then increased.On the whole,the relative importance of stochastic component was significantly larger in plant community(0.552±0.035;mean±standard error)than in microbial community(0.427±0.035).Consistently,the proportion of compositional variation explained by the deterministic soil and community indices was smaller for plant community(0.172–0.186)than microbial community(0.240–0.767).Meanwhile,as nitrogen addition rate increased,the linkage between plant and microbial community composition first became weaker and then became stronger.The larger stochasticity in plant community relative to microbial community assembly suggested that more stochastic strategies(e.g.,seeds addition)should be adopted to maintain above-than below-ground biodiversity under the pressure of nitrogen deposition.
基金supported by the National Natural Science Foundation of China(51767017)the Basic Research Innovation Group Project of Gansu Province(18JR3RA133)the Industrial Support and Guidance Project of Universities in Gansu Province(2022CYZC-22).
文摘Photovoltaic (PV) modules, as essential components of solar power generation systems, significantly influence unitpower generation costs.The service life of these modules directly affects these costs. Over time, the performanceof PV modules gradually declines due to internal degradation and external environmental factors.This cumulativedegradation impacts the overall reliability of photovoltaic power generation. This study addresses the complexdegradation process of PV modules by developing a two-stage Wiener process model. This approach accountsfor the distinct phases of degradation resulting from module aging and environmental influences. A powerdegradation model based on the two-stage Wiener process is constructed to describe individual differences inmodule degradation processes. To estimate the model parameters, a combination of the Expectation-Maximization(EM) algorithm and the Bayesian method is employed. Furthermore, the Schwarz Information Criterion (SIC) isutilized to identify critical change points in PV module degradation trajectories. To validate the universality andeffectiveness of the proposed method, a comparative analysis is conducted against other established life predictiontechniques for PV modules.
基金National Natural Science Foundation of China(72101085)China Postdoctoral Science Foundation funded project(2022M722355)Laboratory of Computation and Analytics of Complex Management Systems(CACMS)(Tianjin University)the Natural Science Foundation of Shandong Province(ZR2022MG086).
文摘Laboratory experiments are one of the important means used to investigate travel choice behavior under strategic uncertainty.Many experiment-based studies have shown that the Nash equilibrium can predict aggregated route choices,while the fluctuations,whose mechanisms are still unclear,continue to exist until the end.To understand the fluctuations,this paper proposes a route-dependent attraction-based stochastic process model,which shares exactly the same behavioral foundation introduced in Part I of the study(Qi et al.,2023),i.e.,route-dependent inertia and route-dependent preference.The model predictions are carefully compared with the experimental observations obtained from the congestible parallel-route laboratory experiments containing 312 subjects and eight decision-making scenarios(Qi et al.,2023).The results show that the proposed stochastic process model can precisely reproduce the random oscillations both in terms of flow switching and route flow evolution.Subsequently,an approximated model is developed to enhance the efficiency in evaluating the equilibrium distribution,providing a practical tool to evaluate the impacts of transportation policies in both long-and short-term runs.To the best of our knowledge,this paper is the first attempt to model and explain experimental phenomena by introducing stochastic process theories,as well as a successful example of applying experimental economics methodology to improve our understanding of human travel choice behavior.
基金supported by the National Natural Science Foundation of China(No.42007428)the National Forage Industry Technology System Program of China(No.CARS34)+1 种基金the Key Research and Development Program of Shaanxi,China(No.2022SF-285)Shaanxi Province Forestry Science and Technology Innovation Program,China(No.SXLK2022-02-14)。
文摘Effective vegetation reconstruction plays a vital role in the restoration of desert ecosystems.However,in reconstruction of different vegetation types,the community characteristics,assembly processes,and functions of different soil microbial taxa under environmental changes are still disputed,which limits the understanding of the sustainability of desert restoration.Hence,we investigated the soil microbial community characteristics and functional attributes of grassland desert(GD),desert steppe(DS),typical steppe(TS),and artificial forest(AF)in the Mu Us Desert,China.Our findings confirmed the geographical conservation of soil microbial composition but highlighted decreased microbial diversity in TS.Meanwhile,the abundance of rare taxa and microbial community stability in TS improved.Heterogeneous and homogeneous selection determined the assembly of rare and abundant bacterial taxa,respectively,with both being significantly influenced by soil moisture.In contrast,fungal communities displayed stochastic processes and exhibited sensitivity to soil nutrient conditions.Furthermore,our investigation revealed a noteworthy augmentation in bacterial metabolic functionality in TS,aligning with improved vegetation restoration and the assemblage of abundant bacterial taxa.However,within nutrient-limited soils(GD,DS,and AF),the assembly dynamics of rare fungal taxa assumed a prominent role in augmenting their metabolic capacity and adaptability to desert ecosystems.These results highlighted the variations in the assembly processes and metabolic functions of soil microorganisms during vegetation reestablishment and provided corresponding theoretical support for anthropogenic revegetation of desert ecosystems.
基金supported by the Horizon Europe Framework Programme(HORIZON),call Teaming for Excellence(HORIZONWIDERA-2022-ACCESS-01-two-stage)-Creation of the Centre of Excellence in Smart Forestry“Forest 4.0”No.101059985″This research was cofunded by FOREST 4.0-“Ekscelencijos centras tvariai miško bioekonomikai vystyti”(Nr.10-042-P-0002).
文摘Models that predict a forest stand’s evolution are essential for developing plans for sustainable management.A simple mathematical framework was developed that con-siders the individual tree and stand basal area under random resource competition and is based on two assumptions:(1)a sigmoid-type stochastic process governs tree and stand basal area dynamics of living and dying trees,and(2)the total area that a tree may potentially occupy determines the number of trees per hectare.The most effective method to satisfy these requirements is formalizing each tree diameter and potentially occupied area using Gompertz-type stochastic differential equations governed by fixed and mixed-effect parameters.Data from permanent experimental plots from long-term Lithuania experiments were used to construct the tree and stand basal area models.The new models were relatively unbiased for live trees of all species,including silver birch(Betula pen-dula Roth)and downy birch(Betula pubescens Ehrh.),[spruce(Picea abies),and pine(Pinus sylvestris)].Less reliable predic-tions were made for the basal area of dying trees.Pines gave the highest accuracy prediction of mean basal area among all live trees.The mean basal area prediction for all dying trees was lower than that for live trees.Among all species,pine also had the best average basal area prediction accuracy for live trees.Newly developed basal area growth and yield models can be recommended despite their complex formulation and implementation challenges,particularly in situations when data is scarce.This is because the newly observed plot provides sufficient information to calibrate random effects.
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
基金supported by the National Key Research and Development Program of China(Grant No.2018YFB0905200)the National NaturalScience Foundation of China(Grant Nos.51577096,51677100&51761135015)
文摘With the increasing penetration of renewable energy resources(RESs), the uncertainties of volatile renewable generations significantly affect the power system operation. Such uncertainties are usually modeled as stochastic variables obeying specific distributions by neglecting the temporal correlations. Conventional approaches to hedge the negative effects caused by such uncertainties are thus hard to pursue a trade-off between computation efficiency and optimality. As an alternative, the theory of stochastic process can naturally model temporal correlation in closed forms. Attracted by this feature, our research group has been conducting thorough researches in the past decade to introduce stochastic processes within renewable power systems. This paper summarizes our works from the perspective of both the frequency domain and the time domain, provides the tools for the analysis and control of power systems under a unified framework of stochastic processes, and discusses the underlying reasons that stochastic process-based approaches can perform better than conventional approaches on both computational efficiency and optimality. These work may shed a new light on the research of analysis, control and operation of renewable power systems.Finally, this paper outlooks the theoretic developments of stochastic processes in future’s renewable power systems.
基金the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050217007)
文摘Stochastic process algebras have been proposed as compositional specification formalisms for performance models. A formal analysis method of survivable network was proposed based on stochastic process algebra, which incorporates formal modeling into performance analysis perfectly, and then various performance parameters of survivable network can be simultaneously obtained after formal modeling. The formal description with process expression to the survivable network system was carried out based on the simply introduced syntax and operational semantics of stochastic process algebra. Then PEPA workbench tool was used to obtain the probability of system’s steady state availability and transient state availability. Simulation experiments show the effectiveness and feasibility of the developed method.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korean government(No.NRF-2018R1C1B6007755)supported by a grant(No.20SCIPC158976-01)from the Construction Technology Research Program funded by the Ministry of Land,Infrastructure,and Transport of the Korean government+2 种基金the Natural Science Foundation of Guangxi,China(No.2018GXNSFDA 281006)the National Natural Science Foundation of China(No.41966005)the One Hundred Talents Project of Guangxi,China(No.6020303891251)。
文摘Nematodes play an important role in ecosystems;however,very little is known about their assembly processes and the factors influencing them.We studied nematode communities in bulk soils from three Asian mountain ecosystems to determine the assembly processes of free-living nematode metacommunities and their driving factors.On each mountain,elevations span a range of climatic conditions with the potential to reveal assembly processes that predominate across multiple biomes.A phylogenetic null modeling framework was used to analyze 18S rRNA gene amplicons to quantify various assembly processes.We found that phylogenetic turnover between nematode communities on all mountains was dominated by stochastic processes,with“undominated processes”being the most predominant stochastic factor.Elevation has a significant impact on the relative importance of deterministic and stochastic processes.A variety of climatic and edaphic variables significantly influenced the variations in community assembly processes with elevation,even though their impacts were not consistent between the mountains.Overall,our results indicate that free-living nematode metacommunities in a wide range of environments are largely structured by stochastic processes rather than by niche-based deterministic processes,suggesting that metacommunities of soil free-living nematodes may respond to climate change in a largely unpredictable way.
文摘The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set valued stochastic processes are obtained.
