Large deviation principles for stochastic nonlinear Schrodinger equations driven by Levy noise

Abstract

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schr\"{o}dinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative L\'evy noise in the Marcus canonical form. This task is challenging in the current setting due to the presence of the power-type nonlinear term, the lack of regularization effect of the Schr\"odinger operator and the absence of compactness of embeddings. To overcome these difficulties, we employ a regularization procedure based on Yosida approximations and implement techniques such as time discretization, cut-off arguments, and relative entropy estimates of sequences of probability measures. Our innovative approach circumvents the need for compactness conditions, distinguishing our work from previous studies.