On solutions of backward stochastic differential equations with jumps, with unbounded stopping times as terminal and with non-lipschitz coefficients, and probabilistic interpretation of quasi-linear elliptic type integro-differential equations

The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non-Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi-linear elliptic type integro-differential equations is obtained.