Weak Solvability Theorem for Forward-Backward SDEs
Abstract
We establish the existence and uniqueness of weak solutions to a suitable class of non-degenerate FBSDEs with a one-dimensional backward component. The classical Lipschitz framework is weakened: the diffusion matrix and the final condition are space Holder continuous whereas the drift and the backward driver may be discontinuous in x. The growth of the backward driver is also allowed to be at most quadratic with respect to the gradient term.
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