On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. (English) Zbl 1058.60042

Summary: We prove a result of existence and uniqueness of solutions to forward-backward stochastic differential equations, with non-degeneracy of the diffusion matrix and boundedness of the coefficients as functions of \(x\) as main assumptions. This result is proved in two steps. The first part studies the problem of existence and uniqueness over a small enough time duration, whereas the second one explains, by using the connection with quasi-linear parabolic system of PDEs, how we can deduce, from this local result, the existence and uniqueness of a solution over an arbitrarily prescribed time duration. Improving this method, we obtain a result of existence and uniqueness of classical solutions to non-degenerate quasi-linear parabolic systems of PDEs. This approach relaxes the regularity assumptions required on the coefficients by the four-step scheme.


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