Optimal Hoeffding bounds for discrete reversible Markov chains

Optimal Hoeffding bounds for discrete reversible Markov chains

Carlos A. León and François Perron

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

Abstract

We build optimal exponential bounds for the probabilities of large deviations of sums ∑_k=1ⁿf(X_k) where (X_k) 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.

Primary Subjects: 65C05

Keywords: Large deviations; Markov chains; Chernoff bounds; Perron–Frobenius eigenvalue

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737118
Digital Object Identifier: doi:10.1214/105051604000000170
Mathematical Reviews number (MathSciNet): MR2052909

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