Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations

Details Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations

2011-09-04

arxiv.org/abs/1109.0672v1

Mathematics

Probability

23 pages

Scientific paper

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) 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 in short) is established, which can be regarded as an extension of Feynman-Kac formula to non-Markov frame.

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