Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

Journal of Mathematical Physics (Impact Factor: 1.3). 09/2004; DOI: 10.1063/1.1318734
Source: arXiv

ABSTRACT The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of particles whose motion is governed by a {\em nonlinear} Langevin-type equation, which is driven by a non-Gaussian Levy-stable noise. We obtain in fact a more general result for Markovian processes generated by stochastic differential equations.}

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May 20, 2014