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

Kai Du and Qi Zhang

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1616-1637

Abstract: 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.

Keywords: Backward stochastic partial differential equations; Semi-linear degenerate equations; Forward–backward stochastic differential equations; Feynman–Kac formula (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1616-1637

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DOI: 10.1016/j.spa.2013.01.005

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