Exit Times of Symmetric Stable Processes from Unbounded Convex Domains

Abstract

We provide several inequalities on the asymptotic behavior of the harmonic measure of the first exit position of a $d$-dimensional symmetric stable process from a unbounded convex domain. Our results on the harmonic measure will determine the asymptotic behavior of the distributions of the first exit time from the domain. These inequalities are given in terms of the growth of the inradius of the cross sections of the domain.