Poisson Limit Theorem for Countable Markov Chains in Markovian Environments

FANG Da-fan; WANG Han-xing; TANG Mao-ning

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Article Navigation > Applied Mathematics and Mechanics > 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.

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.

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Poisson Limit Theorem for Countable Markov Chains in Markovian Environments

1.
Department of Mathematics, Yueyang Normal University, Hunan 414000, P. R. China;
2.
Department of Mathematics, Shanghai University, Shanghai 2000436, P. R. China

Received Date: 2001-07-19
Rev Recd Date: 2002-12-10
Publish Date: 2003-03-15

Abstract

Abstract

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.
- Poisson distributions,
- Markov chains,
- random environments

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References(8)

References

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