Semi-linear degenerate backward stochastic partial differential equations and associated forward backward stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Du, Kai¹  Zhang, Qi¹ 

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

关键词: Backward stochastic partial differential equations;    Semi-linear degenerate equations;    Forward-backward stochastic differential equations;    Feynman-Kac formula;   

DOI  :  10.1016/j.spa.2013.01.005

来源: Elsevier

【 摘 要 】

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman-Kac formula to the non-Markovian framework. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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