The Annals of Applied Probability

Optimal Hoeffding bounds for discrete reversible Markov chains

Carlos A. León and François Perron

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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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 2 (2004), 958-970.

Dates
First available in Project Euclid: 23 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1082737118

Digital Object Identifier
doi:10.1214/105051604000000170

Mathematical Reviews number (MathSciNet)
MR2052909

Zentralblatt MATH identifier
1056.60070

Subjects
Primary: 65C05: Monte Carlo methods

Keywords
Large deviations Markov chains Chernoff bounds Perron–Frobenius eigenvalue

Citation

A. León, Carlos; Perron, François. Optimal Hoeffding bounds for discrete reversible Markov chains. Ann. Appl. Probab. 14 (2004), no. 2, 958--970. doi:10.1214/105051604000000170. https://projecteuclid.org/euclid.aoap/1082737118


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