Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients

Abstract : We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang 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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ESAIM: Probability and Statistics, EDP Sciences, 2006, 10, pp.184-205
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Contributeur : Romain Abraham <>
Soumis le : vendredi 9 septembre 2005 - 12:34:53
Dernière modification le : vendredi 17 novembre 2017 - 15:30:04
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Romain Abraham, Olivier Rivière. Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients. ESAIM: Probability and Statistics, EDP Sciences, 2006, 10, pp.184-205. 〈hal-00008569〉

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