Generalized Fokker-Planck equation: Derivation and exact solutions

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dc.creatorDenisov, S. I.
dc.creatorHorsthemke, Werner
dc.creatorHänggi, Peter
dc.date2008-08-02
dc.date2009-04-29
dc.date.accessioned2026-07-07T13:09:11Z
dc.date.available2026-07-07T13:09:11Z
dc.descriptionWe 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0808.0274
dc.identifierhttp://arxiv.org/abs/0808.0274
dc.identifierEur. Phys. J. B 68, 567 (2009)
dc.identifierdoi:10.1140/epjb/e2009-00126-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228652
dc.subjectStatistical Mechanics
dc.titleGeneralized Fokker-Planck equation: Derivation and exact solutions
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