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2020 A quantitative McDiarmid’s inequality for geometrically ergodic Markov chains
Antoine Havet, Matthieu Lerasle, Eric Moulines, Elodie Vernet
Electron. Commun. Probab. 25: 1-11 (2020). DOI: 10.1214/20-ECP286

Abstract

We state and prove a quantitative version of the bounded difference inequality for geometrically ergodic Markov chains. Our proof uses the same martingale decomposition as [2] but, compared to this paper, the exact coupling argument is modified to fill a gap between the strongly aperiodic case and the general aperiodic case.

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Antoine Havet. Matthieu Lerasle. Eric Moulines. Elodie Vernet. "A quantitative McDiarmid’s inequality for geometrically ergodic Markov chains." Electron. Commun. Probab. 25 1 - 11, 2020. https://doi.org/10.1214/20-ECP286

Information

Received: 5 July 2019; Accepted: 7 January 2020; Published: 2020
First available in Project Euclid: 10 February 2020

zbMATH: 1434.60174
MathSciNet: MR4069735
Digital Object Identifier: 10.1214/20-ECP286

Subjects:
Primary: 60E15 , 60J05

Keywords: Concentration inequalities , coupling , geometric ergodicity , Markov chains

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