The stochastic nonlinear Schrödinger equations driven by pure jump noise

Abstract

In this paper, we establish the existence and uniqueness of solutions of stochastic nonlinear Schrödinger equations with additive jump noise in $L^2({\mathbb{R}}^d)$. Our results cover all either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case.