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Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations
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.Comment: 23 page
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