Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 29-41
A non-nonstandard proof of Reimers' existence result for heat SPDEs
Duke University, Mathematics Department, Durham 27708, NC, USA
Received 1 November 1996; Revised 1 July 1997
Copyright © 1998 Hassan Allouba. 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 1989, Reimers gave a nonstandard proof of the existence of a solution to
heat SPDEs, driven by space-time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non-nonstandard proof of this fact,
and with the aid of Girsanov's theorem for continuous orthogonal martingale measures (proved in a separate paper by the author), the result is extended to the case of a measurable drift.