On some stochastic parabolic differential equations in a Hilbert space (Q2495093)

Summary: We consider some stochastic difference partial differential equations of the form \(du(x,t,c)=L(x,t,D)u(x,t,c)dt+M(x,t,D)u(x,t-a,c)dw(t)\), where \(L(x,t,D)\) is a linear uniformly elliptic partial differential operator of the second order, \(M(x,t,D)\) is a linear partial differential operator of the first order, and \(w(t)\) is a Wiener process. The existence and uniqueness of the solution of suitable mixed problems are studied for the considered equation. Some properties are also studied. A more general stochastic problem is considered in a Hilbert space and the results concerning stochastic partial differential equations are obtained as applications.