Lévy flights in inhomogeneous environments

Piotr Garbaczewski and Vladimir Stephanovich

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 21, 4419-4435

Abstract: We study the long time asymptotics of probability density functions (pdfs) of Lévy flights in confining potentials that originate from inhomogeneities of the environment in which the flights take place. To this end we employ two model patterns of dynamical behavior: Langevin-driven and (Lévy–Schrödinger) semigroup-driven dynamics. It turns out that the semigroup modeling provides much stronger confining properties than the standard Langevin one. For computational and visualization purposes our observations are exemplified for the Cauchy driver and its response to external polynomial potentials (referring to Lévy oscillators), with respect to both dynamical mechanisms. We discuss the links of the Lévy semigroup motion scenario with that of random searches in spatially inhomogeneous media.

Keywords: Stochastic processes; Lévy flights; Lévy–Schrödinger semigroup; Langevin equations; Confining potentials (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:21:p:4419-4435

DOI: 10.1016/j.physa.2010.06.036

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