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arXiv · 0908.2695

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Xicheng Zhang
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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 $L^1$-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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Xicheng Zhang. 2009-08-24. Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients. https://arxiv.org/abs/0908.2695

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