Hitting times of points and intervals for symmetric Lévy processes

Tomasz Grzywny, Michał Ryznar

Published 2015-01-19Version 1

For one-dimensional symmetric L\'{e}vy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is either a single point or an interval. The estimates are obtained under some weak type scaling assumptions on the characteristic exponent of the process. We apply these results to prove optimal estimates of the transition density of the process killed after hitting B.