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2008•Advances in MathematicsRequires access

Some Strong Limit Theorems of Markov Chains in Markovian Environments

Yangli Hu, Suming Wang

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Abstract

Some strong limit theorems of Markov chains in Markovian environments are studied by analysis method.And a strong limit theorem for the functions of four variables related to these chains is obtained.As corollaries,some limit properties of relative entropy density of Markov chains in Markovian environments are gotten.Finally,the Shannon theorem to the case of Markov chains in Markovian environments is promoted.

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What this paper is about

Some strong limit theorems of Markov chains in Markovian environments are studied by analysis method.And a strong limit theorem for the functions of four variables related to these chains is obtained.As corollaries,some limit properties of relative entropy density of Markov chains in Markovian environments are gotten.Finally,the Shannon theorem to the case of Markov chains in Markovian environments is promoted.

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Available abstract

Some strong limit theorems of Markov chains in Markovian environments are studied by analysis method.And a strong limit theorem for the functions of four variables related to these chains is obtained.As corollaries,some limit properties of relative entropy density of Markov chains in Markovian environments are gotten.Finally,the Shannon theorem to the case of Markov chains in Markovian environments is promoted.

Key concepts: Markov chain, Mathematics, Examples of Markov chains, Markov process, Limit (mathematics), Markov chain mixing time, Balance equation, Markov kernel

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