Polynomial deviation bounds for recurrent Harris processes having general state space

Abstract

Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc, Fort and Guillin (2009) introduced verifiable conditions in terms of a supermartingale property implying an explicit control of modulated moments of hitting times. We show how this control can be translated into a control of polynomial moments of abstract regeneration times which are obtained by using the coupling method of Nummelin, extended to the time-continuous context. As a consequence, if a p th moment of the regeneration times exists, then we obtain non asymptotic deviation bounds of the form