Levy flights and Levy -Schroedinger semigroups

Details Levy flights and Levy -Schroedinger semigroups Levy flights and Levy -Schroedinger semigroups

2009-02-20

arxiv.org/abs/0902.3536v3

Cent. Eur. J. Phys, 8(5), 699-708, (2010)

Physics

Condensed Matter

Statistical Mechanics

To appear in Cent. Eur. J. Phys. (2010)

Scientific paper

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.

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