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

Let (Xn)n≥1(Xn)n≥1 be a Markov chain on a general state space with stationary distribution ππ 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.