Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 167-173

On some stochastic parabolic differential equations in a Hilbert space

Khairia El-Said El-Nadi

Department of Mathematics, Faculty of Science, Alexandria University, P.O. Box 21511, Alexandria, Egypt

Received 12 March 2004; Revised 29 July 2004

Copyright © 2005 Khairia El-Said El-Nadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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,ta,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 Weiner 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.