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Optimal Hoeffding bounds for discrete reversible Markov chains

Carlos A. Leon·Francois Perron
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Abstract

We build optimal exponential bounds for the probabilities of large deviations of sums \sum_{k=1}^nf(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 E_πf, the end-points of the support of f, the sample size n and the second largest eigenvalue λof the transition matrix.

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BibTeXRIS

Carlos A. Leon, Francois Perron. 2004-05-14. Optimal Hoeffding bounds for discrete reversible Markov chains. https://doi.org/10.1214/105051604000000170

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