数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 505-530.doi: 10.1007/s10473-023-0203-7

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A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE*

Ran Wang, Beibei Zhang   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2021-11-16 修回日期:2022-04-27 出版日期:2023-03-25 发布日期:2023-04-12
  • 通讯作者: †Ran Wang, E-mail: rwang@whu.edu.cn.
  • 作者简介:Beibei Zhang, zhangbb@whu.edu.cn
  • 基金资助:
    The research of Wang was partially supported by the National Natural Science Foundation of China (11871382, 12071361), the research of Zhang was partially supported by the National Natural Science Foundation of China (11971361, 11731012).

A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE*

Ran Wang, Beibei Zhang   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2021-11-16 Revised:2022-04-27 Online:2023-03-25 Published:2023-04-12
  • Contact: †Ran Wang, E-mail: rwang@whu.edu.cn.
  • About author:Beibei Zhang, zhangbb@whu.edu.cn
  • Supported by:
    The research of Wang was partially supported by the National Natural Science Foundation of China (11871382, 12071361), the research of Zhang was partially supported by the National Natural Science Foundation of China (11971361, 11731012).

摘要: 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 and the jump noise. Here, we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle, which was initially proposed by Matoussi, Sabbagh and Zhang (2021).

关键词: large deviation principle, weak convergence method, stochastic generalized Ginzburg-Landau equation, Poisson random measure

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 and the jump noise. Here, we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle, which was initially proposed by Matoussi, Sabbagh and Zhang (2021).

Key words: large deviation principle, weak convergence method, stochastic generalized Ginzburg-Landau equation, Poisson random measure