HAL : inria-00001228, version 1

DOI : 10.1016/j.spa.2003.09.012

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Stochastic Processes and their Applications 110, 1 (2004) 145-176

A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE

Antoine Lejay 1, 2

(2004)

We extend some results on time-homogeneous processes generated by divergence form operators to time-inhomogeneous ones. These results concern the decomposition of such processes as Dirichlet process, with an explicit expression for the term of zero-quadratic variation. Moreover, we extend some results on the Itô formula and BSDEs related to weak solutions of PDEs, and we study the case of quasi-linear PDEs. Finally, our results are used to prove the existence of weak solutions to forward–backward stochastic differential equations.

1 :	OMEGA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II
2 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine

Domaine

:

Mathématiques/Probabilités

Mots-clés : Quasi-linear PDE – Divergence form-operator – Forward–backward stochastic differential equation – Time reversal of a diffusion – Dirichlet process

inria-00001228, version 1

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Contributeur : Antoine Lejay <>

Soumis le : Lundi 10 Avril 2006, 21:57:05

Dernière modification le : Dimanche 10 Septembre 2006, 10:15:27