Asymptotics for occupation times of half-lines by stable processes and perturbed reflecting brownian motion

Abstract

We derive the integral tests for the sample path behaviour of the occupation times of half-lines by reflecting Brownian motion perturbed by its local time at zero (i.e. , where B; is a linear Brownian motion, l its local time at 0 and μ positive constant) and stable processes, which correspond to the generalized Arcsine laws which have been derived for such processes