Lévy flights and Lévy-Schrödinger semigroups

• Authors: Piotr Garbaczewski
• Languages of publication: EN

Abstracts

EN

We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological Lévy process with the same invariant pdf and in reverse.

Keywords

EN

symmetric stable noise; Lévy flights; Lévy semigroups; Schrödinger boundary data problem; stationary densities; Cauchy noise; confining potentials

Discipline

• 05.40.Jc: Brownian motion
• 02.50.Ey: Stochastic processes
• 05.20.-y: Classical statistical mechanics
• 05.10.Gg: Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

• Journal: Open Physics
• Year: 2010
• Volume: 8
• Issue: 5
• Pages: 699-708

Dates

published

1 - 10 - 2010

online

22 - 7 - 2010

Contributors

author

Piotr Garbaczewski

• Institute of Physics, University of Opole, 45-052, Opole, Poland,

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Identifiers

DOI

10.2478/s11534-009-0156-z