Lp-solution of backward doubly stochastic differential equations

Auguste Aman (1)

1 LMAI - Laboratoire de Mathématiques Appliquées et Informatique

In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BDSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions, extending the results of Pardoux and Peng \cite{PP1} to the case where the solution is taked in $L^{p},\, p>1$ and the monotonicity conditions are satisfied. This study is limited to deterministic terminal time.

Mots clés: $p$-integrable data.; Backward doubly stochastic differential equations; monotone generator; $p$-integrable data

Domaines: Probabilités [math.PR]

Auguste Aman. Lp-solution of backward doubly stochastic differential equations. 2009. ⟨hal-00285154v5⟩