Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

2009/08/19 by Xicheng Zhang, Zhang, Xicheng
Computer Science · Mathematics · #35K15 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35K15 #msc:60H15

paper · pdf · doi:10.48550/arxiv.0908.2695

32

openalex publication_date 2009/08/19 · arxiv created 2009/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, using DiPerna-Lions theory \citeDi-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 L¹-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.

Related

• A sharp L_p-regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients
• A Class of degenerate Stochastic differential equations with non-Lipschitz coefficients
• W^m,p-Solution (p≥2) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space
• L²-Theory of Linear Degenerate SPDEs and L^p (p>0) Estimates for the Uniform Norm of Weak Solutions
• Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients