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Sensitivity and convergence of uniformly ergodic Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

A. Yu. Mitrophanov
A. Yu. Mitrophanov*
Affiliation:
Saratov State University
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Abstract

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For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improve upon the bounds obtained by other authors. We discuss convergence bounds that hold in the case of finite state space, and consider numerical examples to compare the accuracy of different perturbation bounds.

Keywords

Markov chainuniform ergodicityrate of convergenceergodicity coefficientperturbation boundsensitivity analysis

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J35: Transition functions, generators and resolvents
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1003 - 1014
Copyright
© Applied Probability Trust 2005 

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