Bsde's with Jumps and Associated Integro{partial Diierential Equations Etienne Pardoux Small Latp, Ura Cnrs 225

0 Introduction Backward Stochastic Diierential Equations (in short BSDE's) are new type of stochastic diierential equations, whose terminal value is a given random variable, which have been introduced in particular by Pardoux, Peng in 5]. They have proved to be useful models in Mathematical Finance, see Bar-les, Buckdahn, Pardoux 2] and the references therein. In 6], it has been show that BSDE's provide probabilistic formulas for solutions of certain quasilinear partial diierential equations. The papers 5] and 6] deal with BSDE's with respect to the Brownian motion, and associated second order parabolic PDE's. The aim of this paper is to generalize those results to BSDE's with respect to both Brownian mo