Excursions away from a regular point for one-dimensional symmetric Levy processes without Gaussian part

Abstract

The characteristic measure of excursions away from a regular point is studied for a class of symmetric L\'evy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result is applied to prove extremeness of the excursion measure and to prove several sample path behaviors of the excursion and the $ h $-path processes.