On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case
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.
Year of publication: |
2002
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Authors: | Delarue, François |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 99.2002, 2, p. 209-286
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Publisher: |
Elsevier |
Keywords: | Existence and uniqueness Forward-backward stochastic differential equations Gradient estimate Quasi-linear equations of parabolic type |
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