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

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arxiv math/0409486 v1 pith:O5QGRPMB submitted 2004-09-24 math.AP math-phmath.MP

D. Schertzer , M. Larchev , J. Duan , V.V. Yanovsky , S. Lovejoy This is my paper · ORCID
classification math.APmath-phmath.MP
keywords equationdifferentialdrivenequationsstochasticfokker--planckfractionalnoises
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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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  1. Benign Overfitting Does Not Occur in Diffusion Models

    stat.ML 2026-07 conditional novelty 7.0 of 10

    Benign overfitting and double descent do not occur in diffusion models: population and empirical score-matching losses cannot both be small without exponentially many samples.

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