The Annals of Applied Probability

Chernoff-type bound for finite Markov chains

Pascal Lezaud

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This paper develops bounds on the distribution function of the empirical mean for irreducible finite-state Markov chains. One approach, explored by Gillman, reduces this problem to bounding the largest eigenvalue of a perturbation of the transition matrix for the Markov chain. By using estimates on eigenvalues given in Kato's book Perturbation Theory for Linear Operators, we simplify the proof of Gillman and extend it to nonreversible finite-state Markov chains and continuous time. We also set out another method, directly applicable to some general ergodic Markov kernels having a spectral gap.

Article information

Ann. Appl. Probab. Volume 8, Number 3 (1998), 849-867.

First available in Project Euclid: 9 August 2002

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Primary: 60F10: Large deviations

Markov chain Chernoff bound eigenvalues perturbation theory


Lezaud, Pascal. Chernoff-type bound for finite Markov chains. Ann. Appl. Probab. 8 (1998), no. 3, 849--867. doi:10.1214/aoap/1028903453.

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