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Stability and exponential convergence of continuous-time Markov chains

Part of: Stability theory Distribution theory - Probability Basic linear algebra Markov processes

Published online by Cambridge University Press:  14 July 2016

A. Yu. Mitrophanov
A. Yu. Mitrophanov*
Affiliation:
Saratov State University
*
∗Postal address: Faculty of Computer Science and Information Technology, Saratov State University, 83 Astrakhanskaya str., Saratov 410012, Russia. Email address: mitrophanovay@info.sgu.ru
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Abstract

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

Keywords

Markov chainexponential convergenceperturbation boundssensitivity analysisergodicity coefficienteigenvaluespectral gap

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents 60E15: Inequalities; stochastic orderings 34D10: Perturbations 15A42: Inequalities involving eigenvalues and eigenvectors
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 970 - 979
Copyright
Copyright © Applied Probability Trust 2003 

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