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
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
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
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
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 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
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
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
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
In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system ...In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather than remains stable. However, from a practical point of view, it is always preferred to apply the simplest method to address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model to analyze the failure data from real repairable systems. A graphic method and the Laplace test were also used in the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entire life cycle of repairable systems.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
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
Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is inve...Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.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
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
Concrete is considered as an elastic body when subjected to compressive stress butas a brittle body when subjected to tensile stress. That is, after the elastic extremum it cannotcontinue to bear the stress. Based on ...Concrete is considered as an elastic body when subjected to compressive stress butas a brittle body when subjected to tensile stress. That is, after the elastic extremum it cannotcontinue to bear the stress. Based on this.'cracked' physical model, for stochastic extemalwind loads, nonlinear stochastic constitutive equations have been established. To solve equations of nonlinear stochastic vibration, an iterative statistic linearization method (ISLM) hasbeen developedb. Some statistic characteristics were foundd out.展开更多
We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript.We are comparing the solutions of stochastic and deterministic computer virus models.Outcomes of a thr...We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript.We are comparing the solutions of stochastic and deterministic computer virus models.Outcomes of a threshold number R0 hold in stochastic computer virus model.If R_(0)<1 then in such a condition virus controlled in the computer population while R_(0)>1 shows virus rapidly spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties.On this basis,we can suggest a collection of strategies for removing virus’s propagation in the computer population.展开更多
This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequflibrium transitions induced ...This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequflibrium transitions induced by the cross- correlated noises are studied. The stationary solutions of the Fokker-Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.展开更多
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.
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.
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.
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.
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.
文摘In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather than remains stable. However, from a practical point of view, it is always preferred to apply the simplest method to address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model to analyze the failure data from real repairable systems. A graphic method and the Laplace test were also used in the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entire life cycle of repairable systems.
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 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.
基金supported by the Natural Science Foundation of Heilongjiang Province(No.F200504)
文摘Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.
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Concrete is considered as an elastic body when subjected to compressive stress butas a brittle body when subjected to tensile stress. That is, after the elastic extremum it cannotcontinue to bear the stress. Based on this.'cracked' physical model, for stochastic extemalwind loads, nonlinear stochastic constitutive equations have been established. To solve equations of nonlinear stochastic vibration, an iterative statistic linearization method (ISLM) hasbeen developedb. Some statistic characteristics were foundd out.
文摘We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript.We are comparing the solutions of stochastic and deterministic computer virus models.Outcomes of a threshold number R0 hold in stochastic computer virus model.If R_(0)<1 then in such a condition virus controlled in the computer population while R_(0)>1 shows virus rapidly spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties.On this basis,we can suggest a collection of strategies for removing virus’s propagation in the computer population.
基金Project supported by the Fund for Less Developed Regions of the National Natural Science Foundation of China (Grant No. 10864009)the Natural Science Foundation of Yunnan Province,China (Grant No. 2008CD109)
文摘This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequflibrium transitions induced by the cross- correlated noises are studied. The stationary solutions of the Fokker-Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.
