6533b825fe1ef96bd1281e92

RESEARCH PRODUCT

Lévy flights and Lévy-Schrödinger semigroups

Piotr Garbaczewski

subject

QC1-999FOS: Physical sciencesGeneral Physics and Astronomy05.40.jcLévy process05.20.-yMaster equationFOS: MathematicsInvariant (mathematics)cauchy noiseCondensed Matter - Statistical MechanicsMathematical PhysicsMathematical physicsMathematicslévy semigroupsStationary distributionStatistical Mechanics (cond-mat.stat-mech)02.50.eyPhysicsProbability (math.PR)symmetric stable noisestationary densitiesMathematical Physics (math-ph)Function (mathematics)lévy flightsLangevin equationconfining potentialsLévy flight05.10.ggschrödinger boundary data problemConservative forceMathematics - Probability

description

We analyze two different confining mechanisms for L\'{e}vy 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 Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy 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 L\'{e}vy process with the very same invariant pdf and in the reverse.

https://doi.org/10.2478/s11534-009-0156-z