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

S.B. Connor and G. Fort

Stochastic Processes and their Applications, 2009, vol. 119, issue 12, 4176-4193

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 in Connor and Kendall (2007) [2] 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.

Keywords: Markov; chains; Foster-Lyapunov; functions; State-dependent; drift; conditions; Regularity; Tame; chains; Networks; of; queues (search for similar items in EconPapers)
Date: 2009
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