Uniqueness and absolute continuity of weak solutions for parabolic SPDE's |
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| Authors: | R Mikulevi?ius B L Rozovskii |
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| Institution: | (1) Center for Applied Mathematical Sciences, University of Southern California, 90089-1113 Los Angeles, CA, USA;(2) Present address: Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania |
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| Abstract: | The paper presents necessary and sufficient conditions for the absolute continuity of measures generated by infinite-dimensional martingale problems. This result is applied to the study of the existence and uniqueness of weak solutions to nonlinear parabolic SPDE's. The paper also addresses the problem of stochastic integration with respect to a martingale in a quasi-complete locally convex topological vector space.This work was partially supported by NSF Grant # DMS-9002997 and ONR Grant # N00014-91-J-1526. |
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| Keywords: | 60H15 60H05 60G44 |
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