Cauchy flights in confining potentials

Piotr Garbaczewski

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 5, 936-944

Abstract: We analyze confining mechanisms for Lévy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target pdf (eventually asymptotic) equals the preselected one. To this end, dynamically distinct jump-type processes can be employed. We demonstrate that one “targeted stochasticity” scenario involves Langevin systems with a symmetric stable noise. Another derives from the Lévy–Schrödinger semigroup dynamics (closely linked with topologically induced super-diffusions), which has no standard Langevin representation. For computational and visualization purposes, the Cauchy driver is employed to exemplify our considerations.

Keywords: Levy flights; Langevin equation; Cauchy–Schrödinger semigroup; Reverse engineering problem; Targeted stochasticity; Stationary pdf; Fractional transport equations; Confining potentials; Confined Cauchy flights (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:5:p:936-944

DOI: 10.1016/j.physa.2009.11.021

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