Langevin equation with super-heavy-tailed noise

Details Langevin equation with super-heavy-tailed noise Langevin equation with super-heavy-tailed noise

2010-03-06

arxiv.org/abs/1003.1406v2

J. Phys. A: Math. Theor. 43, 285004 (2010)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 3 figures

Scientific paper

10.1088/1751-8113/43/28/285004

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker-Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorbed, that are equivalent to those for a classical particle in an absorbing medium. The connection between the rate of absorption and the super-heavy-tailed distribution of the increments is established analytically. A numerical scheme for the simulation of the Langevin equation with super-heavy-tailed noise is developed and used to verify our theoretical results.

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