On solutions of backward stochastic differential equations with jumps and applications (Q1382509)

Existence and uniqueness results are obtained for a backward stochastic differential equation with jumps, with bounded (random) stopping time as a terminal time and with non-Lipschitz coefficients. The coefficients are assumed to be jointly continuous and satisfying the sublinear growth condition and a weaker form of monotonicity condition. Also, a convergence result (a kind of continuous dependence of solutions on coefficients of the equation) is proved. In the second part of the paper, a Feynman-Kac type formula is derived by means of a generalized Itô lemma. By virtue of this formula a probabilistic interpretation of solutions to partial differential and integral equations is found and existence results are given.