Resumen de Stable processes have thorns

Krzysztof Burdzy, Tadeusz Kulczycki

• Let X(t) be the symmetric α-stable process in \R, α∈(0,2), d ≥ 2. For f\dvtx(0,1)→(0,∞) let D(f) be the thorn {x∈\R\dvtxx1∈(0,1),\allowbreak|(x2,…,xd)| < f(x1)}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s)+D¯¯¯¯(f) for all t∈[s,s+1).