Fractional diffusion limit for a stochastic kinetic equation

Sylvain de Moor (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Kinetic equations; diffusion limit; perturbed test functions; fractional diffusion

Mots clés: stochastic partial differential equations; fractional diffusion.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Sylvain de Moor. Fractional diffusion limit for a stochastic kinetic equation. Stochastic Processes and their Applications, 2014, Volume 124 (Issue 3), pp.Pages 1335-1367. ⟨10.1016/j.spa.2013.11.007⟩. ⟨hal-00906247⟩