Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Xicheng Zhang

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Probability 2009-08-24 v2 Analysis of PDEs

Authors: Xicheng Zhang

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.

Keywords

stochastic differential equations partial differential equations ordinary differential equations

Cite

@article{arxiv.0908.2695,
  title  = {Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients},
  author = {Xicheng Zhang},
  journal= {arXiv preprint arXiv:0908.2695},
  year   = {2009}
}

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