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

被引：10

作者：

Connor, S. B. ^{[1
]}

Fort, G. ^{[2
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] TELECOM ParisTech, CNRS, LTC1, F-75634 Paris 13, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 12期

关键词：

Markov chains; Foster-Lyapunov functions; State-dependent drift conditions; Regularity; Tame chains; Networks of queues; MULTICLASS QUEUING-NETWORKS; STABILITY; RATES; ERGODICITY;

D O I：

10.1016/j.spa.2009.10.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：4176 / 4193

页数：18

共 20 条

[1]

[Anonymous], 2007, THESIS U WARWICK

[2]

[Anonymous], 2003, STOCHASTIC MODELLING

[3] Perfect simulation for a class of positive recurrent markov chains (vol 17, pg 781, 2007) [J].

Connor, Stephen B. ;

Kendall, Wilfrid S. .

ANNALS OF APPLIED PROBABILITY, 2007, 17 (5-6) :1808-1810

[4] ON THE CONVERGENCE OF MULTICLASS QUEUEING NETWORKS IN HEAVY TRAFFIC [J].

Dai, J. G. ;

Vien Nguyen .

ANNALS OF APPLIED PROBABILITY, 1994, 4 (01) :26-42

[5] ON POSITIVE HARRIS RECURRENCE OF MULTICLASS QUEUEING NETWORKS: A UNIFIED APPROACH VIA FLUID LIMIT MODELS [J].

Dai, J. G. .

ANNALS OF APPLIED PROBABILITY, 1995, 5 (01) :49-77

[6] STABILITY AND CONVERGENCE OF MOMENTS FOR MULTICLASS QUEUING-NETWORKS VIA FLUID LIMIT MODELS [J].

DAI, JG ;

MEYN, SP .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (11) :1889-1904

[7] Practical drift conditions for subgeometric rates of convergence [J].

Douc, R ;

Fort, G ;

Moulines, E ;

Soulier, P .

ANNALS OF APPLIED PROBABILITY, 2004, 14 (03) :1353-1377

[8]

DOUC R, 2009, STOCHASTIC PROCESS A

[9] Subgeometric ergodicity of strong Markov processes [J].

Fort, G ;

Roberts, GO .

ANNALS OF APPLIED PROBABILITY, 2005, 15 (02) :1565-1589

[10] Polynomial ergodicity of Markov transition kernels [J].

Fort, G ;

Moulines, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 103 (01) :57-99

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