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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [8 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00008569
Contributor : Romain Abraham <>
Submitted on : Friday, September 9, 2005 - 12:34:53 PM
Last modification on : Friday, September 20, 2019 - 4:34:02 PM
Long-term archiving on: Thursday, April 1, 2010 - 8:57:32 PM

Identifiers

  • HAL Id : hal-00008569, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

289

Files downloads

349