Open Access
Translator Disclaimer
August 1998 Chernoff-type bound for finite Markov chains
Pascal Lezaud
Ann. Appl. Probab. 8(3): 849-867 (August 1998). DOI: 10.1214/aoap/1028903453


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.


Download Citation

Pascal Lezaud. "Chernoff-type bound for finite Markov chains." Ann. Appl. Probab. 8 (3) 849 - 867, August 1998.


Published: August 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0938.60027
MathSciNet: MR1627795
Digital Object Identifier: 10.1214/aoap/1028903453

Primary: 60F10

Keywords: Chernoff bound , Eigenvalues , Markov chain , Perturbation theory

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 3 • August 1998
Back to Top