First exit times from a bounded interval for L\'{e}vy processes

Abstract

In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents. We also study the cumulative distribution function of the supremum and infimum processes. Finally, we establish integral conditions that assure that the renewal function of the ladder height process is comparable with the linear one.