Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space

Let (Xn)n≥1 be a Markov chain on a general state space with stationary distribution π and a spectral gap in the space Lπ2. In this paper, we prove that the probabilities of large deviations of sums Sn=∑k=1nf(Xk) satisfy an inequality of Hoeffding type. We generalize results of León and Perron (2004) in two directions; in our paper the state space is general and we do not assume reversibility.

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Year of publication:	2014
Authors:	Miasojedow, Błażej
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 87.2014, C, p. 115-120
Publisher:	Elsevier
Subject:	Hoeffding’s inequality \| Markov chains \| Spectral gap \| Geometric ergodicity

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040066