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arXiv · 1311.4743

Fractional diffusion limit for a stochastic kinetic equation

Sylvain De Moor
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Abstract

We study the stochastic fractional diffusive limit of a kinetic equation involving a small parameter and perturbed by a smooth random term. Generalizing the method of perturbed test functions, under an appropriate scaling for the small parameter, and with the moment method used in the deterministic case, we show the convergence in law to a stochastic fluid limit involving a fractional Laplacian.

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Sylvain De Moor. 2013-11-19. Fractional diffusion limit for a stochastic kinetic equation. https://doi.org/10.1016/j.spa.2013.11.007

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