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2008•Stochastic Analysis and ApplicationsRequires access

On the Ergodicity of Slow-Varying Nonstationary Markov Chains

Jinn-Wen Wu, Kuo-Chih Chen

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Abstract

We consider a nonstationary Markov chain: X(k + 1) = P(k)X(k), where and P(k) is a stochastic matrix for all k = 0,1,2,…. The main purpose of this article is to present some new conditions to guarantee the ergodicity for slow-varying nonstationary Markov chains and the bound for variation of ‖P(k + 1) − P(k)‖1 to ensure the strongly ergodicity is constructed as well.

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What this paper is about

We consider a nonstationary Markov chain: X(k + 1) = P(k)X(k), where and P(k) is a stochastic matrix for all k = 0,1,2,…. The main purpose of this article is to present some new conditions to guarantee the ergodicity for slow-varying nonstationary Markov chains and the bound for variation of ‖P(k + 1) − P(k)‖1 to ensure the strongly ergodicity is constructed as well.

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Available abstract

We consider a nonstationary Markov chain: X(k + 1) = P(k)X(k), where and P(k) is a stochastic matrix for all k = 0,1,2,…. The main purpose of this article is to present some new conditions to guarantee the ergodicity for slow-varying nonstationary Markov chains and the bound for variation of ‖P(k + 1) − P(k)‖1 to ensure the strongly ergodicity is constructed as well.

Key concepts: Ergodicity, Markov chain, Mathematics, Examples of Markov chains, Statistical physics, Markov process, Stochastic matrix, Markov renewal process

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