Caractérisation de la dispersion avec un modèle fractionnaire

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian 1 noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be relevant in different domains of Physics. We therefore derive in this paper a Fractional Fokker-Planck equation for the probability distribution of particles whose motion is governed by a nonlinear Langevin-type equation, which is driven by a Levy-stable noise rather than a Gaussian. We obtain in fact a general result for a Markovian forcing. We also discuss the existence and uniqueness of the solution of the Fractional Fokker-Planck equation.

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Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

Schertzer

Larchev

Duan

et al. 2001

Journal of Mathematical Physics

185

180

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Caractérisation de la dispersion avec un modèle fractionnaire

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References 12 publications

Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

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