Stochastic partial differential equations with unbounded and degenerate coefficients

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Zhang, Xicheng^1,2 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

关键词: DiPerna-Lions theory;    Stochastic partial differential equation;    Maximal principle;    Nonlinear filtering;   

DOI  :  10.1016/j.jde.2010.11.021

来源: Elsevier

【 摘 要 】

In this article, using DiPerna-Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate nonsmooth 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. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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