Forward-backward Stochastic Differential Equations and Pde with Gradient Dependent Second Order Coefficients
نویسندگان
چکیده
We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for which the assumptions are easy to check. Mathematics Subject Classification. 60H10, 60H30. Received June 17, 2004. Revised June 17, and September 12, 2005.
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