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Solutions to general forward-backward doubly stochastic differential equations. (English) Zbl 1166.60318

Summary: A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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