The Adapted Solutions for Backward Stochastic Schrödinger Equations with Jumps

This study considers a class of backward stochastic semi-linear Schrödinger equations with Poisson jumps in Rd or in its bounded domain of a C2 boundary, which is associated with a stochastic control problem of nonlinear Schrödinger equations driven by Lévy noise. The approach to establish the existence and uniqueness of solutions is mainly based on the complex Itô formula, the Galerkin’s approximation method, and the martingale representation theorem.