Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
979112 | Physica A: Statistical Mechanics and its Applications | 2010 | 9 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Piotr Garbaczewski,