Generalized Fokker-Planck equation: Derivation and exact solutions
作者： W. Horsthemke , P. Hänggi , S. I. Denisov , S. I. Denisov
DOI: 10.1140/EPJB/E2009-00126-3
关键词: White noise 、 Statistical physics 、 Stochastic process 、 Physics 、 Poisson's equation 、 Fokker–Planck equation 、 Mathematical analysis 、 Quadratic equation 、 Langevin equation 、 Multiplicative noise 、 Noise (electronics)
摘要: We derive the generalized Fokker-Planck equation associated with Langevin (in Ito sense) for an overdamped particle in external potential driven by multiplicative noise arbitrary distribution of increments generating process. explicitly consider this various specific types noises, including Poisson white and Levy stable noise, show that it reproduces all equations are known these noises. Exact analytical, time-dependent stationary solutions derived analyzed detail cases a linear, quadratic, tailored potential.
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