This paper studies the comparison theorem of forward-backward differential equations with Poisson jumps(FBSDEJ for short). We use a purely probabilistic approch including stopping time techneque and iteration method to prove comparison theorem. Here we only investigate some classes of FBSDEJs...

Existence and uniqueness is established for solutions to backward stochastic differential equations with jumps and non-Lipschitzian coefficients in Hilbert space. The results are used to solve some special types of optimal stochastic control problems with respect to certain BSDEs with jumps in...

For backward stochastic differential equation (BSDE) with jumps and with non-Lipschitzian coefficient the existence and uniqueness of an adapted solution is obtained. By generalizing the existence result on partial differential and integral equations (PDIE) and Ito formula to the functions with...