Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Details Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

2009-08-19

arxiv.org/abs/0908.2695v2

Mathematics

Probability

32

Scientific paper

In this article, using DiPerna-Lions theory \cite{Di-Li}, we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the $L^1$-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.

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