Generalized Fokker-Planck equation: Derivation and exact solutions
Generalized Fokker-Planck equation: Derivation and exact solutions
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DOI：
10.1140/epjb/e2009-00126-3
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发表时间：
2009-04-01
影响因子：
1.6
通讯作者：
Haenggi, P.
中科院分区：
文献类型：
--
作者：
Denisov, S. I.;Horsthemke, W.;Haenggi, P.
我们推导了与朗之万方程（在伊藤意义上）相关的广义福克-普朗克方程，用于由乘性噪声驱动的外部势中的过阻尼粒子，噪声生成过程的增量具有任意分布。我们针对各种特定类型的噪声（包括泊松白噪声和 L,vy 稳定噪声）明确考虑该方程，并表明它再现了这些噪声已知的所有 Fokker-Planck 方程。针对线性、二次和定制势的情况，导出并详细分析了广义 Fokker-Planck 方程的精确解析、瞬态和平稳解。
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.