an:06781811
Zbl 1371.60081
Garbaczewski, Piotr; ??aba, Mariusz
Nonlocal random motions and the trapping problem
EN
Acta Phys. Pol. B 46, No. 2, 231-246 (2015).
00370364
2015
j
60G51
Summary: L??vy 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 L??vy 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 this issue for an exemplary case of the Cauchy process in a finite interval. Qualitatively, our observations extend to general jump-type processes that are driven by non-Gaussian noises, classified by the integral part of the L??vy-Khintchine formula. For clarity of arguments, we discuss, as a reference model, the classic case of the Brownian motion in the interval.