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(Xk) where (Xk) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean
the end-points of the support of f, the sample size n and the second largest eigenvalue λ of the transition matrix.
Keywords: Large deviations; Markov chains; Chernoff bounds; Perron–Frobenius eigenvalue
Full-text: Access granted (open access)
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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