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

Stochastic Processes and their Applications, 2004, vol. 110, issue 1, 145-176

Abstract: 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.

Keywords: Quasi-linear; PDE; Divergence; form-operator; Forward-backward; stochastic; differential; equation; Time; reversal; of; a; diffusion; Dirichlet; process (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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