Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 2, Pages 115-138
doi:10.1155/S1048953395000128
Weak infinitesimal generator for a stochastic partial
differential equation with time delay
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.
Abstract
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.