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

Abstract

Abstract Let ( X n ) n ≥ 1 be a Markov chain on a general state space with stationary distribution π and a spectral gap in the space L π 2 . In this paper, we prove that the probabilities of large deviations of sums S n = ∑ k = 1 n f ( X k ) satisfy an inequality of Hoeffding type. We generalize results of Leon and Perron (2004) in two directions; in our paper the state space is general and we do not assume reversibility.