Large deviation principle for stochastic generalized Ginzburg-Landau equation driven by jump noise

TL;DR

This paper proves a large deviation principle for a stochastic generalized Ginzburg-Landau equation influenced by jump noise, overcoming challenges posed by non-linear coefficients using a novel weak convergence criterion.

Contribution

It introduces a new sufficient condition for weak convergence, enabling the establishment of large deviation principles for complex stochastic PDEs with jump noise.

Findings

Established large deviation principle for the equation

Overcame difficulties from highly non-linear coefficients

Utilized a new weak convergence criterion

Abstract

In this paper, we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise. The main difficulties come from the highly non-linear coefficient. Here we adopt a new sufficient condition for the weak convergence criteria, which is proposed by Matoussi, Sabbagh and Zhang (2021).