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2014•Communication in Statistics- Theory and MethodsRequires access

Strong Law of Large Numbers for Countable Asymptotic Circular Markov Chains

Weiguo Yang, Bei Wang, Zhiyan Shi

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Abstract

In this article, we introduce the notion of a countable asymptotic circular Markov chain, and prove a strong law of large numbers: as a corollary, we generalize a well-known version of the strong law of large numbers for nonhomogeneous Markov chains, and prove the Shannon-McMillan-Breiman theorem in this context, extending the result for the finite case.

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What this paper is about

In this article, we introduce the notion of a countable asymptotic circular Markov chain, and prove a strong law of large numbers: as a corollary, we generalize a well-known version of the strong law of large numbers for nonhomogeneous Markov chains, and prove the Shannon-McMillan-Breiman theorem in this context, extending the result for the finite case.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this article, we introduce the notion of a countable asymptotic circular Markov chain, and prove a strong law of large numbers: as a corollary, we generalize a well-known version of the strong law of large numbers for nonhomogeneous Markov chains, and prove the Shannon-McMillan-Breiman theorem in this context, extending the result for the finite case.

Key concepts: Markov chain, Countable set, Corollary, Law of large numbers, Mathematics, Context (archaeology), Markov process, Examples of Markov chains

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