Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations
Copyright policy )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.
23 pages
- Fudan University China (People's Republic of)
- University of Wollongong Australia
equa, associated, differential, semi-linear degenerate equations, Probability (math.PR), backward, forward, Feynman-Kac formula, degenerate, backward stochastic partial differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), semi, linear, Stochastic partial differential equations (aspects of stochastic analysis), tions, forward-backward stochastic differential equations, equations, partial, FOS: Mathematics, stochastic, Mathematics - Probability
equa, associated, differential, semi-linear degenerate equations, Probability (math.PR), backward, forward, Feynman-Kac formula, degenerate, backward stochastic partial differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), semi, linear, Stochastic partial differential equations (aspects of stochastic analysis), tions, forward-backward stochastic differential equations, equations, partial, FOS: Mathematics, stochastic, Mathematics - Probability
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