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Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients
Published online by Cambridge University Press: 09 March 2006
Abstract
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.
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- © EDP Sciences, SMAI, 2006
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