37 research outputs found
Hitting times of points and intervals for symmetric L\'{e}vy processes
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.Comment: 39 page