Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains

Randal Douc; Arnaud Guillin; Eric Moulines

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Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains

Randal Douc·Arnaud Guillin·Eric Moulines

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Abstract

This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster-Lyapunov conditions. The regeneration-split chain method and a precise control of the modulated moment of the hitting time to small sets are employed in the proof.

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Randal Douc, Arnaud Guillin, Eric Moulines. 2006-01-03. Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains. https://arxiv.org/abs/math/0601036

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