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 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
Modeling urban land-use dynamics is critical for urban experts’and infrastructure managers’planning.This study attempts to explore the land-use/land-cover(LULC)dynamics of Gondar using satellite images from 1984 to ...Modeling urban land-use dynamics is critical for urban experts’and infrastructure managers’planning.This study attempts to explore the land-use/land-cover(LULC)dynamics of Gondar using satellite images from 1984 to 2020.Markov-Chain and Cellular Automata(MC-CA)models have been recognized as performing well in predicting urban land-use change.However,only a few models work in Ethiopia in general,and no study in Gondar has applied this approach to study urban land-use patterns.Therefore,Gondar land-use/land cover changes of Gondar were predicted using the MC-CA model in IDRISI.The built-up area in Gondar city covered 1413 ha(3%of the total area)in 1984 and increased to 2380 ha(5%)in 1994;21153 ha(45.5%)in 2004;22622 ha(48.7%)in 2014;and 23427 ha(50.5%)in 2020.The area has been predicted to reach 57.5%in the 2050s,showing a faster increase that will cause a very vast loss of farmland.This will increase urban sprawl challenges as well as overall environmental disequilibrium in the preceding decade.Thus,innovative and careful structures and systems in urban planning are required to secure a sustainable urban future and to make our cities livable and competitive in the paradigm of sustainable cities.展开更多
The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-F...The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.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
A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two re...A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.展开更多
This paper explores the current English vocabulary teaching classroom based on an eco-linguistic perspective and the Markov chain,points out the ecological imbalance in the English vocabulary classroom,and proposes me...This paper explores the current English vocabulary teaching classroom based on an eco-linguistic perspective and the Markov chain,points out the ecological imbalance in the English vocabulary classroom,and proposes measures to solve the problem and strategies to build an ecological English vocabulary learning classroom,in order to provide some reference for future English vocabulary curriculum reform and curriculum design.In this paper,a random sample of 20 students from each class was taken from an advanced arts class and an advanced science class.The results show that after a semester of teaching process,the overall English scores of the arts and science classes improved,and since,the arts classes improved more and the teachers’teaching quality was better.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
为提高智能网联(connected and automated,CA)卡车、小车及人工驾驶卡车、小车的混合流道路通行能力,提出基于排强度和渗透率的CA车辆单独编队和合作编队策略.分别设计两种策略下混合流车辆跟驰模式,推导出基于改进Markov模型,涵盖CA车...为提高智能网联(connected and automated,CA)卡车、小车及人工驾驶卡车、小车的混合流道路通行能力,提出基于排强度和渗透率的CA车辆单独编队和合作编队策略.分别设计两种策略下混合流车辆跟驰模式,推导出基于改进Markov模型,涵盖CA车辆渗透率和排强度的车辆状态转移概率;分析两种策略下CA车辆队列分布,建立各策略下的混合流道路容量模型,并通过理论证明和仿真实验予以验证.结果表明,与不编队策略相比,两种策略下道路容量分别提高1.23%~49.62%和1.47%~60.34%,合作编队策略与单独编队策略相比能将道路容量再提高11%;当CA车辆渗透率大于50%和排强度大于0时,编队策略对道路容量的提升效果更显著,容量能提高13.27%~60.34%;单独编队策略下CA小车和CA卡车最大队列规模分别为8辆和6辆,合作编队下CA车辆最大队列规模为8辆.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
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Modeling urban land-use dynamics is critical for urban experts’and infrastructure managers’planning.This study attempts to explore the land-use/land-cover(LULC)dynamics of Gondar using satellite images from 1984 to 2020.Markov-Chain and Cellular Automata(MC-CA)models have been recognized as performing well in predicting urban land-use change.However,only a few models work in Ethiopia in general,and no study in Gondar has applied this approach to study urban land-use patterns.Therefore,Gondar land-use/land cover changes of Gondar were predicted using the MC-CA model in IDRISI.The built-up area in Gondar city covered 1413 ha(3%of the total area)in 1984 and increased to 2380 ha(5%)in 1994;21153 ha(45.5%)in 2004;22622 ha(48.7%)in 2014;and 23427 ha(50.5%)in 2020.The area has been predicted to reach 57.5%in the 2050s,showing a faster increase that will cause a very vast loss of farmland.This will increase urban sprawl challenges as well as overall environmental disequilibrium in the preceding decade.Thus,innovative and careful structures and systems in urban planning are required to secure a sustainable urban future and to make our cities livable and competitive in the paradigm of sustainable cities.
基金National Natural Science Foundation of China(No.11671258)。
文摘The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.
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A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.
文摘This paper explores the current English vocabulary teaching classroom based on an eco-linguistic perspective and the Markov chain,points out the ecological imbalance in the English vocabulary classroom,and proposes measures to solve the problem and strategies to build an ecological English vocabulary learning classroom,in order to provide some reference for future English vocabulary curriculum reform and curriculum design.In this paper,a random sample of 20 students from each class was taken from an advanced arts class and an advanced science class.The results show that after a semester of teaching process,the overall English scores of the arts and science classes improved,and since,the arts classes improved more and the teachers’teaching quality was better.
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.
文摘为提高智能网联(connected and automated,CA)卡车、小车及人工驾驶卡车、小车的混合流道路通行能力,提出基于排强度和渗透率的CA车辆单独编队和合作编队策略.分别设计两种策略下混合流车辆跟驰模式,推导出基于改进Markov模型,涵盖CA车辆渗透率和排强度的车辆状态转移概率;分析两种策略下CA车辆队列分布,建立各策略下的混合流道路容量模型,并通过理论证明和仿真实验予以验证.结果表明,与不编队策略相比,两种策略下道路容量分别提高1.23%~49.62%和1.47%~60.34%,合作编队策略与单独编队策略相比能将道路容量再提高11%;当CA车辆渗透率大于50%和排强度大于0时,编队策略对道路容量的提升效果更显著,容量能提高13.27%~60.34%;单独编队策略下CA小车和CA卡车最大队列规模分别为8辆和6辆,合作编队下CA车辆最大队列规模为8辆.
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。
