Exponential Moments for Hitting Times of Uniformly Ergodic Markov Processes

Abstract

Let $\mu$ be an invariant measure for a Markov process which is assumed $\mu$-uniformly ergodic in the following sense: the corresponding semigroup of operators on $L^2(d\mu)$, say $\{P_t; t \geq 0\}$, is such that the time average $(1/T) \int^T_0 P_t dt$ converges to a rank one projection in the uniform norm of operators. We prove that hitting times of sets having non zero $\mu$-measure possess moment generating functions.