The stochastic nonlinear Schr\"{o}dinger equations driven by pure jump noise

TL;DR

This paper proves the existence and uniqueness of solutions for stochastic nonlinear Schrödinger equations driven by pure jump noise, covering all subcritical nonlinearities in the full range of exponents, extending deterministic results.

Contribution

It establishes the well-posedness of stochastic nonlinear Schrödinger equations with jump noise for all subcritical nonlinearities, a significant extension of deterministic theory.

Findings

Existence and uniqueness of solutions in L^2(R^d)

Applicable to both focusing and defocusing nonlinearities

Covers full subcritical exponent range

Abstract

In this paper, we establish the existence and uniqueness of solutions of stochastic nonlinear Schr\"{o}dinger 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.