Resumen de Symmetric stable processes stay in thick sets

Jang-Mei Wu

• Let X(t) be the symmetric α-stable process in Rd(0 < α < 2,d≥2). Then let W(f) be the thorn {x ∈ Rd\dvtx0 < x1 < 1,(x22+⋯+x2d)1/2 < f(x1)} where f\dvtx(0,1) →(0,1) is continuous, increasing with f(0+) = 0. Recently Burdzy and Kulczycki gave an exact integral condition on f for the existence of a random time s such that X(t) remains in the thorn X(s)+W(f)¯¯¯¯¯¯¯¯¯¯¯¯ for all t∈[s,s+1). We extend their theorem to general open sets W with 0∈∂W. In general, α-processes may stay in sets which are quite lacunary and are not locally connected at 0.