Escape from bounded domains driven by multi-variate $α$-stable noises

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $α$-stable Lévy 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 $α$ describing jumps' length asymptotics both for spherical and Cartesian Lévy flights. Finally, we study escape from $d$-dimensional hyper-sphere showing that $d$-dimensional escape process can be used to discriminate between various types of multi-variate $α$-stable noises, especially spherical and Cartesian Lévy flights.

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