Generalized Fokker-Planck equation: Derivation and exact solutions

被引：0
|
作者：
S. I. Denisov
W. Horsthemke
P. Hänggi
机构：
[1] Max-Planck-Institut für Physik komplexer Systeme,Department of Chemistry
[2] Sumy State University,undefined
[3] Southern Methodist University,undefined
[4] Institut für Physik,undefined
[5] Universität Augsburg,undefined
[6] Universitätsstraße 1,undefined
来源：
The European Physical Journal B | 2009年 / 68卷
关键词：
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion; 05.10.Gg Stochastic analysis methods; 02.50.-r Probability theory, stochastic processes, and statistics;
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摘要：
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.
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页码：567 / 575
页数：8
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