Optimal Hoeffding bounds for discrete reversible Markov chains

Details Optimal Hoeffding bounds for discrete reversible Markov chains Optimal Hoeffding bounds for discrete reversible Markov chains

2004-05-14

arxiv.org/abs/math/0405296v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 958-970

Mathematics

Probability

Scientific paper

10.1214/105051604000000170

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_{\pi}f, the end-points of the support of f, the sample size n and the
second largest eigenvalue \lambda of the transition matrix.

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