On solutions of backward stochastic differential equations with jumps and with non-Lipschitzian coefficients in Hilbert spaces and stochastic control

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 Hilbert space. The existence of some non-Lipschitzian optimal controls is also established.