We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The co...We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.展开更多
This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founde...This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founders of mathematical geology.He was the fi rst to defi ne mathematical geology as“a scientifi c discipline concerned with the construction,analysis and use of conceptual mathematical models of geological events to solve concrete problems”(Vistelius in Principles of mathematical geology,Nauka,Leningrad,1980;Principles of mathematical geology,Kluwer Academic Publishers,Dordrecht,1992).Mathematical models in this context should be primarily probabilistic because of the large number of infl uencing natural factors.They must be conceptual to avoid fundamental errors in application.Vistelius devoted his seminal book to geological random sequences and their description and analysis using Markov models as stochastic tools.He applied this approach to grain sequences in granitic intrusive rocks and to sedimentary rock layers.Among other things,Vistelius has used Markov chain analysis in mineral resource exploration to distinguish between“ideal”granites,which are not subsequently mineralized,and mainly hydrothermally mineralized,sometimes ore-bearing granites which contain at least two generations of main minerals.The application of this special conceptual stochastic model is demonstrated on Lusatian granite(Saxony,Germany).展开更多
This paper studies the existence of the higher orders deviation matrices for continuous time Markov chains by the moments for the hitting times. An estimate of the polynomial convergence rates for the transition matri...This paper studies the existence of the higher orders deviation matrices for continuous time Markov chains by the moments for the hitting times. An estimate of the polynomial convergence rates for the transition matrix to the stationary measure is obtained. Finally, the explicit formulas for birth-death processes are presented.展开更多
We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.展开更多
We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the i...We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.展开更多
Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is propo...Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.展开更多
This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance mi...This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.展开更多
Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of off...Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.展开更多
Kuala Lumpur of Malaysia,as a tropical city,has experienced a notable decline in its critical urban green infrastructure(UGI)due to rapid urbanization and haphazard development.The decrease of UGI,especially natural f...Kuala Lumpur of Malaysia,as a tropical city,has experienced a notable decline in its critical urban green infrastructure(UGI)due to rapid urbanization and haphazard development.The decrease of UGI,especially natural forest and artificial forest,may reduce the diversity of ecosystem services and the ability of Kuala Lumpur to build resilience in the future.This study analyzed land use and land cover(LULC)and UGI changes in Kuala Lumpur based on Landsat satellite images in 1990,2005,and 2021and employed the overall accuracy and Kappa coefficient to assess classification accuracy.LULC was categorized into six main types:natural forest,artificial forest,grassland,water body,bare ground,and built-up area.Satellite images in 1990,2005,and 2021 showed the remarkable overall accuracy values of 91.06%,96.67%,and 98.28%,respectively,along with the significant Kappa coefficient values of 0.8997,0.9626,and 0.9512,respectively.Then,this study utilized Cellular Automata and Markov Chain model to analyze the transition of different LULC types during 1990-2005 and 1990-2021 and predict LULC types in 2050.The results showed that natural forest decreased from 15.22%to 8.20%and artificial forest reduced from 18.51%to 15.16%during 1990-2021.Reductions in natural forest and artificial forest led to alterations in urban surface water dynamics,increasing the risk of urban floods.However,grassland showed a significant increase from 7.80%to 24.30%during 1990-2021.Meanwhile,bare ground increased from 27.16%to 31.56%and built-up area increased from 30.45%to 39.90%during 1990-2005.In 2021,built-up area decreased to 35.10%and bare ground decreased to 13.08%,indicating a consistent dominance of built-up area in the central parts of Kuala Lumpur.This study highlights the importance of integrating past,current,and future LULC changes to improve urban ecosystem services in the city.展开更多
This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persi...This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persistence and allows for combinatorial probability estimations such as initial and transitional probabilities.The hydrologic data was generated(in-situ)and received from Uttarakhand Jal Vidut Nigam Limited(UJVNL),and meteorological data was acquired from NASA’s archives MERRA-2 product.A total of sixteen years(2005-2020)of data was used to foresee daily Precipitation from 2020 to 2022.MERRA-2 products are utilized as observed and forecast values for daily Precipitation throughout the monsoon season,which runs from July to September.Markov Chain and Long Short-Term Memory(LSTM)findings for 2020,2021,and 2022 were observed,and anticipated values for daily rainfall during the monsoon season between July and September.According to test findings,the artificial intelligence technique cannot anticipate future regional meteorological formations;the correlation coefficient R^(2) is around 0.12.According to the randomly verified precipitation data findings,the Markov Chain model has a success rate of 79.17 percent.The results suggest that extended return periods should be a warning sign for drought and flood risk in the Himalayan region.This study gives a better knowledge of the water budget,climate change variability,and impact of global warming,ultimately leading to improved water resource management and better emergency planning to the establishment of the Early Warning System(EWS)for extreme occurrences such as cloudbursts,flash floods,landslides hazards in the complex Himalayan region.展开更多
This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space...This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.展开更多
在多种合理的无信息先验分布下,基于Markov Chain Monte Carlo方法,提出了一种简单且易于抽样的幂律过程的Bayesian分析方法.所提方法将失效、时间截尾数据统一分析,能快捷地获取幂律过程模型参数的Markov Chain Monte Carlo样本,利用...在多种合理的无信息先验分布下,基于Markov Chain Monte Carlo方法,提出了一种简单且易于抽样的幂律过程的Bayesian分析方法.所提方法将失效、时间截尾数据统一分析,能快捷地获取幂律过程模型参数的Markov Chain Monte Carlo样本,利用该样本不但能直接给出模型参数函数的后验分布,还能给出单样预测和双样预测的分析.一个经典工程数值算例说明了所提方法的可行性、合理性与有效性.该方法具有一定的优越性,可为小子样可靠性增长分析提供一种值得参考的方法.展开更多
目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。...目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。展开更多
目的对医院出院病人调查表普遍存在的数据缺失进行填补与分析,以保证统计调查表的质量,为医院以及上级卫生部门了解现状,进行预策和决策提供技术支持和质量保证。方法运用SAS9.1,采用多重填补方法Markov Chain Monte Carlo(MCMC)模型对...目的对医院出院病人调查表普遍存在的数据缺失进行填补与分析,以保证统计调查表的质量,为医院以及上级卫生部门了解现状,进行预策和决策提供技术支持和质量保证。方法运用SAS9.1,采用多重填补方法Markov Chain Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果MCMC填补10次的结果最优。结论(Multiple Imputation)MI方法在解决医院出院病人调查表数据缺失时有优势,发挥空间较大,且填补效率较高。展开更多
基金Acknowledgements The authors would like to thank Professor Yong-Hua Mao for useful discussion. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571372, 11501576, 11771452） and the Excellent Young Scientific Research Fund of Hunan Provincial Education Department （Grant No. 15B252）.
文摘We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.
基金Open Access funding enabled and organized by Projekt DEAL.
文摘This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founders of mathematical geology.He was the fi rst to defi ne mathematical geology as“a scientifi c discipline concerned with the construction,analysis and use of conceptual mathematical models of geological events to solve concrete problems”(Vistelius in Principles of mathematical geology,Nauka,Leningrad,1980;Principles of mathematical geology,Kluwer Academic Publishers,Dordrecht,1992).Mathematical models in this context should be primarily probabilistic because of the large number of infl uencing natural factors.They must be conceptual to avoid fundamental errors in application.Vistelius devoted his seminal book to geological random sequences and their description and analysis using Markov models as stochastic tools.He applied this approach to grain sequences in granitic intrusive rocks and to sedimentary rock layers.Among other things,Vistelius has used Markov chain analysis in mineral resource exploration to distinguish between“ideal”granites,which are not subsequently mineralized,and mainly hydrothermally mineralized,sometimes ore-bearing granites which contain at least two generations of main minerals.The application of this special conceptual stochastic model is demonstrated on Lusatian granite(Saxony,Germany).
基金This work was supported in part by the'973'Projectthe Research Fund for the Doctoral Program of Higher Education(Grant No.20010027007)+1 种基金the National Natural Science Foundation of China(Grant Nos.10121101 and 10301007)the National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10025105).
文摘This paper studies the existence of the higher orders deviation matrices for continuous time Markov chains by the moments for the hitting times. An estimate of the polynomial convergence rates for the transition matrix to the stationary measure is obtained. Finally, the explicit formulas for birth-death processes are presented.
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
基金supported by National Natural Science Foundation of China(Grant No.11211120144)the Fundamental Research Funds for the Central Universities(Grant No.2010QYZD001)
文摘We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.
文摘Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.
基金supported by the National Natural Science Foundation of China(10801056)the Natural Science Foundation of Ningbo(2010A610094)
文摘This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.
文摘Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.
基金supported by the Malaysia-Japan International Institute of Technology(MJIIT),Universiti Teknologi Malaysia.
文摘Kuala Lumpur of Malaysia,as a tropical city,has experienced a notable decline in its critical urban green infrastructure(UGI)due to rapid urbanization and haphazard development.The decrease of UGI,especially natural forest and artificial forest,may reduce the diversity of ecosystem services and the ability of Kuala Lumpur to build resilience in the future.This study analyzed land use and land cover(LULC)and UGI changes in Kuala Lumpur based on Landsat satellite images in 1990,2005,and 2021and employed the overall accuracy and Kappa coefficient to assess classification accuracy.LULC was categorized into six main types:natural forest,artificial forest,grassland,water body,bare ground,and built-up area.Satellite images in 1990,2005,and 2021 showed the remarkable overall accuracy values of 91.06%,96.67%,and 98.28%,respectively,along with the significant Kappa coefficient values of 0.8997,0.9626,and 0.9512,respectively.Then,this study utilized Cellular Automata and Markov Chain model to analyze the transition of different LULC types during 1990-2005 and 1990-2021 and predict LULC types in 2050.The results showed that natural forest decreased from 15.22%to 8.20%and artificial forest reduced from 18.51%to 15.16%during 1990-2021.Reductions in natural forest and artificial forest led to alterations in urban surface water dynamics,increasing the risk of urban floods.However,grassland showed a significant increase from 7.80%to 24.30%during 1990-2021.Meanwhile,bare ground increased from 27.16%to 31.56%and built-up area increased from 30.45%to 39.90%during 1990-2005.In 2021,built-up area decreased to 35.10%and bare ground decreased to 13.08%,indicating a consistent dominance of built-up area in the central parts of Kuala Lumpur.This study highlights the importance of integrating past,current,and future LULC changes to improve urban ecosystem services in the city.
基金This research work was carried out during the SERB,SIRE fellowship (File No.SIR/2022/000972)tenure at Keio University,Japan.
文摘This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persistence and allows for combinatorial probability estimations such as initial and transitional probabilities.The hydrologic data was generated(in-situ)and received from Uttarakhand Jal Vidut Nigam Limited(UJVNL),and meteorological data was acquired from NASA’s archives MERRA-2 product.A total of sixteen years(2005-2020)of data was used to foresee daily Precipitation from 2020 to 2022.MERRA-2 products are utilized as observed and forecast values for daily Precipitation throughout the monsoon season,which runs from July to September.Markov Chain and Long Short-Term Memory(LSTM)findings for 2020,2021,and 2022 were observed,and anticipated values for daily rainfall during the monsoon season between July and September.According to test findings,the artificial intelligence technique cannot anticipate future regional meteorological formations;the correlation coefficient R^(2) is around 0.12.According to the randomly verified precipitation data findings,the Markov Chain model has a success rate of 79.17 percent.The results suggest that extended return periods should be a warning sign for drought and flood risk in the Himalayan region.This study gives a better knowledge of the water budget,climate change variability,and impact of global warming,ultimately leading to improved water resource management and better emergency planning to the establishment of the Early Warning System(EWS)for extreme occurrences such as cloudbursts,flash floods,landslides hazards in the complex Himalayan region.
文摘This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.
文摘在多种合理的无信息先验分布下,基于Markov Chain Monte Carlo方法,提出了一种简单且易于抽样的幂律过程的Bayesian分析方法.所提方法将失效、时间截尾数据统一分析,能快捷地获取幂律过程模型参数的Markov Chain Monte Carlo样本,利用该样本不但能直接给出模型参数函数的后验分布,还能给出单样预测和双样预测的分析.一个经典工程数值算例说明了所提方法的可行性、合理性与有效性.该方法具有一定的优越性,可为小子样可靠性增长分析提供一种值得参考的方法.
文摘目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。
文摘目的对医院出院病人调查表普遍存在的数据缺失进行填补与分析,以保证统计调查表的质量,为医院以及上级卫生部门了解现状,进行预策和决策提供技术支持和质量保证。方法运用SAS9.1,采用多重填补方法Markov Chain Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果MCMC填补10次的结果最优。结论(Multiple Imputation)MI方法在解决医院出院病人调查表数据缺失时有优势,发挥空间较大,且填补效率较高。
