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Large Deviation Bounds for Markov Chains

Published online by Cambridge University Press:  01 December 1997

AT&T Labs–Research, Florham Park, NJ 07932, USA; (e-mail:


We study the fraction of time that a Markov chain spends in a given subset of states. We give an exponential bound on the probability that it exceeds its expectation by a constant factor. Our bound depends on the mixing properties of the chain, and is asymptotically optimal for a certain class of Markov chains. It beats the best previously known results in this direction. We present an application to the leader election problem.

Research Article
1997 Cambridge University Press

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