Probabilistic interpretation for integral-partial differential equations with subdifferential operator (Q2722277)

It is well-known that a solution of quasilinear partial differential equations can be presented as a functional of a solution of some backward stochastic differential equation. This result has been extended to integral-partial differential equations by \textit{G. Barles, R. Buckdahn} and \textit{E. Pardoux} [Stochastics Stochastics Rep. 60, No. 1-2, 57-83 (1997; Zbl 0878.60036)]. Recently \textit{E. Pardoux} and \textit{A. Răşcanu} [Stochastic Processes Appl. 76, No.2, 191-215 (1998; Zbl 0932.60070)] provided a probabilistic interpretation for the viscosity solution of some parabolic and elliptic variational inequalities by using a backward stochastic differential equation involving a sub-differential operator. NEWLINENEWLINENEWLINEThe main aim of this paper is to generalize their result from the parabolic case to the integral-partial variational inequalities through a multivalued backward stochastic differential equation with jumps that is associated with both Brownian motion and Poisson random measure. The key of the proofs is the existence and uniqueness of the solution to multivalued backward stochastic differential equations with jumps which is put in a Markovian framework.