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arXiv · 1406.7096

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

Krzysztof Szczepaniec·Bartlomiej Dybiec
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Abstract

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $\alpha$-stable L\'evy 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 L\'evy 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 $\alpha$-stable noises, especially spherical and Cartesian L\'evy flights.

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Krzysztof Szczepaniec, Bartlomiej Dybiec. 2014-06-27. Escape from bounded domains driven by multi-variate $\alpha$-stable noises. https://doi.org/10.1088/1742-5468/2015/06/p06031

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