Backward stochastic differential equation with random measures (Q1582568)

Let \[ \begin{aligned} Y_t=\xi+ & \int^T_t g(s,Y_s,Z_s) dA_s+\int^T_t \int_Rf\bigl( s,x,Y_s, W(s,x) \bigr) \lambda(ds, dx)\\ & -\int^T_t Z_s dM_s-\int^T_t \int_R Wd (\mu-\nu) \end{aligned} \] be a backward stochastic differential equation (BSDE), where \(M\) is a continuous local martingale, \(A\) is an increasing process, \(\lambda\) and \(\mu\) are random measures, \(\nu\) is the dual predictable projection or compensator of \(\mu\). The author considers the existence and the uniqueness of triplet processes \((Y,Z,W)\) satisfying BSDE. It is also proved the continuous dependence theorem and the comparison theorem.