Optimal Hoeffding bounds for discrete reversible Markov chains
Abstract
We build optimal exponential bounds for the probabilities of large deviations of sums Σk=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 Eπf, the end-points of the support of f, the sample size n and the second largest eigenvalue λ of the transition matrix.
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