On some stochastic parabolic differential equations in a Hilbert space

[摘要] We consider some stochastic difference partial differential equations of the formdu(x,t,c)=L(x,t,D)u(x,t,c)dt+M(x,t,D)u(x,t−a,c)dw(t), whereL(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, andw(t)is a Weiner process. The existence and uniquenessof the solution of suitable mixed problems are studied for theconsidered equation. Some properties are also studied. A moregeneral stochastic problem is considered in a Hilbert space andthe results concerning stochastic partial differential equationsare obtained as applications.

[学科分类] 应用数学