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arXiv · 1412.7320

Nonlocal random motions: The trapping problem

Piotr Garbaczewski·Mariusz Żaba
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Abstract

Lévy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a particular Lévy process may be subject to physically implementable manipulations, whose ultimate goal is to confine the random motion in a spatially finite, possibly mesoscopic trap. We analyze thisissue for an exemplary case of the Cauchy process in a finiteinterval. Qualitatively, our observations extend to general jump-type processes that are driven by non-gaussian noises, classified by the integral part of the Lévy-Khintchine formula.For clarity of arguments we discuss, as a reference model, the classic case of the Brownian motion in the interval.

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Piotr Garbaczewski, Mariusz Żaba. 2015-11-09. Nonlocal random motions: The trapping problem. https://doi.org/10.5506/aphyspolb.46.231

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