On a nonlinear stochastic pseudo-differential equation driven by fractional noise

Abstract

In this paper, we study the existence, uniqueness and Hölder regularity of the solution to a class of nonlinear stochastic pseudo-differential equation of the following form [Formula: see text] where [Formula: see text] is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, the coefficient [Formula: see text] is a measurable function, and [Formula: see text] is a double-parameter fractional noise. In addition, the existence and Gaussian type estimates for the density of the mild solution are proved via Malliavin calculus.