Generalized Fokker-Planck equation: Derivation and exact solutions

被引：73

作者：

Denisov, S. I. ^{[1
,2
]}

Horsthemke, W. ^{[3
]}

Haenggi, P. ^{[4
]}

机构：

[1] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

[2] Sumy State Univ, UA-40007 Sumy, Ukraine

[3] So Methodist Univ, Dept Chem, Dallas, TX 75275 USA

[4] Univ Augsburg, Inst Phys, D-86135 Augsburg, Germany

来源：

EUROPEAN PHYSICAL JOURNAL B | 2009年 / 68卷 / 04期

关键词：

EXTERNAL FORCE-FIELDS; ANOMALOUS DIFFUSION; MASTER-EQUATIONS; LEVY FLIGHTS; LANGEVIN; NOISE; SYSTEMS; DRIVEN; MODELS;

D O I：

10.1140/epjb/e2009-00126-3

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

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 L,vy 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.

引用

页码：567 / 575

页数：9

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