Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

2009/11/02 by Kai Du, Qingxin Meng, Du, Kai +1
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #35R60 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #math.PR #msc:35R60 #msc:60H15

paper · pdf · doi:10.48550/arxiv.0911.0077

20 pages

openalex publication_date 2009/11/02 · arxiv created 2009/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space Hⁿ (=Wⁿ₂) under weaker assumptions than those used by X. Zhou [Journal of Functional Analysis 103, 275--293 (1992)]. As an application, a comparison theorem is obtained.

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