Escape from bounded domains driven by multivariate α-stable noises

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bivariate alpha-stable Levy-type noise from a 2-dimensional disk. For an appropriate choice of parameters the mean first passage time reveals non-trivial, non-monotonous dependence on the stability index alpha describing jumps' length asymptotics both for spherical and Cartesian Levy flights. Finally, we study escape from a d-dimensional hypersphere showing that a d-dimensional escape process can be used to discriminate between various types of multivariate alpha-stable noises, especially spherical and Cartesian Levy flights.