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The spectral gap and perturbation bounds for reversible continuous-time 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

We show that, for reversible continuous-time Markov chains, the closeness of the nonzero eigenvalues of the generator to zero provides complete information about the sensitivity of the distribution vector to perturbations of the generator. Our results hold for both the transient and the stationary states.

Keywords

Markov chainreversibilityeigenvaluespectral gapcondition numberperturbation boundsensitivity analysis

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1219 - 1222
Copyright
Copyright © Applied Probability Trust 2004 

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References

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