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In this paper we provide an analysis of a mean first passage time problem ofa random walker subject to a bi-variate $\alpha$-stable L\'evy type noise froma 2-dimensional disk. For an appropriate choice of parameters the mean firstpassage time reveals non-trivial, non-monotonous dependence on the stabilityindex $\alpha$ describing jumps' length asymptotics both for spherical andCartesian L\'evy flights. Finally, we study escape from $d$-dimensionalhyper-sphere showing that $d$-dimensional escape process can be used todiscriminate between various types of multi-variate $\alpha$-stable noises,especially spherical and Cartesian L\'evy flights.

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