POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS

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POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS

A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.

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作 者: 方大凡 王汉兴 唐矛宁  
作者单位:方大凡(Department of Mathematics, Yueyang Normal University, Yueyang, Hunan 414000, P.R. China;Departnent of Mathematics, Shanghai University, Shanghai 200436, P.R. China)水利论文 LFO5K&j
王汉兴,唐矛宁(Departnent of Mathematics, Shanghai University, Shanghai 200436, P.R. China) 
刊 名:应用数学和力学(英文版)  EI SCI
英文刊名:APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION) 
年,卷(期):2003 24(3) 
分类号:O211.62 
关键词:Poisson distributions   Markov chains   random environments  
机标关键词:MARKOV CHAINSfinite Markov chainsMarkov processlimit theorementropy function 
基金项目:国家自然科学基金 
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