Small stochastic perturbations in a general fractional kinetic equation

Márquez-Carreras, David

ESAIM: Probability and Statistics, Tome 19 (2015), pp. 81-99.

In this paper we study some properties of the density for the law of the solution to a generalized multidimensional fractional kinetic equation driven by a Gaussian noise, white in time and correlated in space. The diffusion operator is the composition between the Bessel and Riesz potentials with any fractional parameters. We also establish Varadhan’s estimates for the solution to the equation obtained by perturbing the noise.

Classification : 60G60, 60H15, 60H30, 60G10, 60G15, 60H07
Mots clés : Stochastic fractional kinetic and heat equation, Bessel and Riesz potentials, small perturbations, density estimates, Malliavin calculus

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