Lévy flights as subordination process: first passage times

Abstract

We obtain the first passage time density for a Lévy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding explicit reference to the fractional diffusion equation. Our results corroborate recent findings for Markovian Lévy flights and generalize to broad waiting times.