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arXiv · 0901.2453

State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains

Stephen B. Connor·Gersende Fort
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Abstract

We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift condition to exist, and use these to partially answer a question posed by Connor & Kendall (2007) concerning the existence of so-called 'tame' Markov chains. Furthermore, we show that our 'subsampled drift condition' implies the existence of finite moments for the return time to a small set.

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Stephen B. Connor, Gersende Fort. 2009-09-03. State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains. https://arxiv.org/abs/0901.2453

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