Volume 19, 2015
|Page(s)||81 - 99|
|Published online||17 June 2015|
Small stochastic perturbations in a general fractional kinetic equation∗
Departament de Probabilitat, Lògica i Estadística, Facultat de
Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007
Revised: 21 January 2014
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.
Mathematics Subject Classification: 60G60 / 60H15 / 60H30 / 60G10 / 60G15 / 60H07
Key words: Stochastic fractional kinetic and heat equation / Bessel and Riesz potentials / small perturbations / density estimates / Malliavin calculus
© EDP Sciences, SMAI, 2015
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