This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations...

In this paper, we obtain a characterization of invariant measures of stochastic evolution equations and stochastic partial differential equations of pure jump type. As an application, it is shown that the equation has a unique invariant probability measure under some reasonable conditions.

In this paper we consider continuity properties of a stochastic heat equation of the form [not partial differential]u(t,x)/[not partial differential]t = [not partial differential]2u(t,x)/[not partial differential]x2 + f(u(t,x))Wx,t. We prove that the solutions of this equation depend...

In this paper, we establish the existence and uniqueness of solutions of systems of stochastic partial differential equations (SPDEs) with reflection in a convex domain. The lack of comparison theorems for systems of SPDEs makes things delicate.

Let be a real-valued fractional Brownian sheet. Consider the (, ) Gaussian random field defined by , where are independent copies of . In this paper, the existence and joint continuity of the local times of are established