Open Access
Translator Disclaimer
May 2004 Optimal Hoeffding bounds for discrete reversible Markov chains
Carlos A. León, François Perron
Author Affiliations +
Ann. Appl. Probab. 14(2): 958-970 (May 2004). DOI: 10.1214/105051604000000170

Abstract

We build optimal exponential bounds for the probabilities of large deviations of sums ∑k=1nf(Xk) where (Xk) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean ${\mathbb {E}}_{\pi}f,$ the end-points of the support of f, the sample size n and the second largest eigenvalue λ of the transition matrix.

Citation

Download Citation

Carlos A. León. François Perron. "Optimal Hoeffding bounds for discrete reversible Markov chains." Ann. Appl. Probab. 14 (2) 958 - 970, May 2004. https://doi.org/10.1214/105051604000000170

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1056.60070
MathSciNet: MR2052909
Digital Object Identifier: 10.1214/105051604000000170

Subjects:
Primary: 65C05

Keywords: Chernoff bounds , large deviations , Markov chains , Perron–Frobenius eigenvalue

Rights: Copyright © 2004 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.14 • No. 2 • May 2004
Back to Top