Document Zbl 0883.60053

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Finding adapted solutions of forward-backward stochastic differential equations: Method of continuation. (English) Zbl 0883.60053

Probab. Theory Relat. Fields 107, No. 4, 537-572 (1997).

Summary: The notion of bridge is introduced for systems of coupled forward-backward stochastic differential equations (FBSDEs, for short). This notion helps us to unify the method of continuation in finding adapted solutions to such FBSDEs over any finite time durations. It is proved that if two FBSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBSDEs.

Cited in 103 Documents

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

coupled forward-backward stochastic differential equations; adapted solutions

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