On Poisson approximation to the partial sum process of a Markov chain

Abstract

This paper gives an upper bound for a Wasserstein distance between the distributions of a partial sum process of a Markov chain and a Poisson process on the positive half line in terms of the transition probabilities and the stationary distribution of the Markov chain. The argument is based on the Stein's method, as adapted for bounds on the distance of the distributions of a point process from a Poisson process in Brown and Xia (1995) (see also Barbour and Brown, 1992), together with a coupling approach.