A non-nonstandard proof of Reimers' existence result for heat SPDEs. (1998)

• Record Type: Journal Article
• Authors: Allouba, Hassan
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 1(1998)
• Page Start: 29
• Page End: 41
• Publication Date: 1998
• Subjects: stochastic PDEs -- stochastic heat equation -- space-time white noise -- martingale problem; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953398000033
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : 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.