Fractional Kinetic Equation Driven by General Space–Time Homogeneous Gaussian Noise

Abstract

In this article, we consider a class of fractional kinetic equation driven by a space–time homogeneous Gaussian noise on $$[0,T]\times {\mathbb {R}}^d$$ with $$T>0$$ . Under some mild assumptions on the spatial spectral measure of the Gaussian noise, we prove the existence of mild solution of this equation (in the Skorohod sense) and the Holder continuity of its sample paths. Our techniques are based on multiple Wiener-Ito integral and Malliavin calculus.