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

TY - JOUR

T1 - State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains

AU - Connor, S. B.

AU - Fort, G.

PY - 2009/12

Y1 - 2009/12

N2 - 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. (C) 2009 Elsevier B.V. All rights reserved.

AB - 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. (C) 2009 Elsevier B.V. All rights reserved.

KW - Markov chains

KW - Foster-Lyapunov functions

KW - State-dependent drift conditions

KW - Regularity

KW - Tame chains

KW - Networks of queues

KW - CONTINUOUS-TIME PROCESSES

KW - STABILITY

KW - RATES

KW - ERGODICITY

UR - http://www.scopus.com/inward/record.url?scp=70350620148&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2009.10.001

DO - 10.1016/j.spa.2009.10.001

M3 - Article

SN - 0304-4149

VL - 119

SP - 4176

EP - 4193

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -