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December 2014 Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes
Aryeh Kontorovich, Roi Weiss
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J. Appl. Probab. 51(4): 1100-1113 (December 2014).

Abstract

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of noncontracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains, which supersedes some of the known results and easily extends to other processes such as Markov trees. As applications, we provide a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

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Aryeh Kontorovich. Roi Weiss. "Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes." J. Appl. Probab. 51 (4) 1100 - 1113, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1320.60060
MathSciNet: MR3301291

Subjects:
Primary: 60E15
Secondary: 60J10

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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