Large deviations for the 2-D derivative Ginzburg–Landau SPDE with multiplicative noise

HUANG Ting; PU Xue-Ke

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Large deviations for the 2-D derivative Ginzburg–Landau SPDE with multiplicative noise

HUANG Ting,PU Xue-Ke *

School of Mathematics and Statistics, Chongqing University, Chongqing 400000

*Correspondence author

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Funding: none

Opened online:26 November 2018

Accepted by: none

Citation: HUANG Ting,PU Xue-Ke.Large deviations for the 2-D derivative Ginzburg–Landau SPDE with multiplicative noise[OL]. [26 November 2018] http://en.paper.edu.cn/en_releasepaper/content/4746507

In this paper, a Wentzell–Freidlin type large deviation principle is established for the 2-D derivative Ginzburg-Landau equation perturbed by a small multiplicative noise. To study the 2-D case, we introduce some Banach space and give some estimates for the stochastic convolution in such a Banach space, and then we prove the LDP bases on the Laplace principle and on weak convergence approach.

Keywords:Large deviations; Stochastic 2-D derivative Ginzburg-Landau equation; Laplace principle; Weak convergence method

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