## 留言板

 引用本文: 方大凡, 王汉兴, 唐矛宁. 马氏环境中可数马氏链的Poisson极限率[J]. 应用数学和力学, 2003, 24(3): 267-274.
FANG Da-fan, WANG Han-xing, TANG Mao-ning. Poisson Limit Theorem for Countable Markov Chains in Markovian Environments[J]. Applied Mathematics and Mechanics, 2003, 24(3): 267-274.
 Citation: FANG Da-fan, WANG Han-xing, TANG Mao-ning. Poisson Limit Theorem for Countable Markov Chains in Markovian Environments[J]. Applied Mathematics and Mechanics, 2003, 24(3): 267-274.

## 马氏环境中可数马氏链的Poisson极限率

###### 作者简介:方大凡(1958- ),男,湖南平江人,副教授,博士.
• 中图分类号: O211.62

## Poisson Limit Theorem for Countable Markov Chains in Markovian Environments

• 摘要: 研究了马氏环境中的可数马氏链,主要证明了过程于小柱集上的回返次数是渐近地服从Poisson分布。为此,引入熵函数h,首先给出了马氏环境中马氏链的Shannon-Mc Millan-Breiman定理,还给出了一个非马氏过程Posson逼近的例子。当环境过程退化为一常数序列时,便得到可数马氏链的Poisson极限定理。这是有限马氏链Pitskel相应结果的拓广。
•  [1] Seyast'yanov B A.Poisson limit law for a scheme of sums of independent random variables[J].Theory of Probability and Its Applications,1972,17(4):695-699. [2] Wang Y H.A Compound poisson Convergence Theorem[J].Ann Probab,1991,19:452-455. [3] Pitskel B.Poisson limit law for markov chains[J].Ergod Th Dynam Sys,1991,11,501-513. [4] Nawrotzki K.Discrete open systems or markov chains is a random environment[J].J Inform Process Cybernet,1981,17:569-599. [5] Nawrotzki K.Discrete open systems or Markov chains in random environment[J].J Inform Process Cybernet,1982,18:83-98. [6] Cogburn R.Markov chains in random environments:the case of Markovian environments[J].Ann Probab,1980,8:908-916. [7] Blum J R,Hanson D L,Koopmans L H.On the strong law of large numbers for a class of stochastic processes[J].Z Wahrsch Verw Gebrete,1963,2:1-11. [8] Cornfeld I,Fomin S,Sinai Ya G.Ergodic Theory[M].New York:Springer-Verlag,1982.

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##### 出版历程
• 收稿日期:  2001-07-19
• 修回日期:  2002-12-10
• 刊出日期:  2003-03-15

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