Uniqueness and absolute continuity of weak solutions for parabolic SPDE's
type: Item
instance of: scholarly article
title: Uniqueness and absolute continuity of weak solutions for parabolic SPDE's
zbMATH Open document ID: 0810.60054
DOI: 10.1007/BF00994917
published in: Acta Applicandae Mathematicae
publication date: 1995-04-04T00:00:00Z
review text: Let \(E\) and \(E'\) be quasicomplete locally convex linear spaces and let \(F\) be a linear subspace of the algebraic dual of \(E'\). In this very general framework the authors define a stochastic integral and introduce martingale problem on the canonical space of \(\sigma (F,E')\)-continuous functions. Then necessary and sufficient conditions are given for absolute continuity of solutions to two different martingale problems. Roughly speaking, it is shown that absolute continuity occurs if and only if the corresponding martingale problems differ in the part of finite variation only. Given absolute continuity of solutions criteria for uniqueness are also obtained. The paper extends all known results on solving martingale problem in infinite dimensions by absolutely continuous change of measure. In the last part of the paper applications to some stochastic partial differential equations are given.
reviewed by: B. Goldys
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 627457
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: martingale problem
zbMATH Keywords: uniqueness
zbMATH Keywords: absolute continuity of measures
zbMATH Keywords: absolute continuity of solutions
author: R. Mikulevicius
author: B. Rozovskii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 627457