Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 2, Pages 115-138

Weak infinitesimal generator for a stochastic partial differential equation with time delay

Mou-Hsiung Chang

University of Alabama in Huntsville, Department of Mathematical Sciences, Huntsville 35899, AL, USA

Received 1 September 1994; Revised 1 March 1995

Copyright © 1995 Mou-Hsiung Chang. 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.


In this paper, we consider the Markov solution process for a stochastic parabolic differential equation with time delay. Under the Lipschitz condition and boundedness on the drift and diffusion coefficient, properties of the weak infinitesimal generator of the associated Markov operators are established. Actions of the weak infinitesimal generator on the space of quasi-tame functions are also investigated.