Concentration of Markov chains with bounded moments

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, pp. 2270-2280, 2019.

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Keywords:
Markov chainsConcentration boundsExpander graphsGillman's theorem

Abstract:

Let {W-t}(t=1)(infinity) be a finite state stationary Markov chain, and suppose that f is a real-valued function on the state space. If f is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for the random variable f (W-1) + . . . + f (W-n) that depend on the spectral gap of the Markov chain and the a...More

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