The Adapted Solutions for Backward Stochastic Schrödinger Equations with Jumps

Li Yang and Lin Liu ()
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Li Yang: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Lin Liu: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China

Mathematics, 2025, vol. 13, issue 5, 1-18

Abstract: This study considers a class of backward stochastic semi-linear Schrödinger equations with Poisson jumps in R d or in its bounded domain of a C 2 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.

Keywords: backward stochastic Schrödinger equation; weak solution; Poisson jump; Galerkin’s finite-dimensional approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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