paper

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

arXiv:0908.2695

Abstract

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 -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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Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients · wovepaper