Open Access
May 2017 Irreducibility of stochastic real Ginzburg–Landau equation driven by $\alpha$-stable noises and applications
Ran Wang, Jie Xiong, Lihu Xu
Bernoulli 23(2): 1179-1201 (May 2017). DOI: 10.3150/15-BEJ773


We establish the irreducibility of stochastic real Ginzburg–Landau equation with $\alpha$-stable noises by a maximal inequality and solving a control problem. As applications, we prove that the system converges to its equilibrium measure with exponential rate under a topology stronger than total variation and obeys the moderate deviation principle by constructing some Lyapunov test functions.


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Ran Wang. Jie Xiong. Lihu Xu. "Irreducibility of stochastic real Ginzburg–Landau equation driven by $\alpha$-stable noises and applications." Bernoulli 23 (2) 1179 - 1201, May 2017.


Received: 1 March 2015; Revised: 1 August 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 06701623
MathSciNet: MR3606763
Digital Object Identifier: 10.3150/15-BEJ773

Keywords: $\alpha$-stable noises , exponential ergodicity , irreducibility , Moderate deviation principle , stochastic real Ginzburg–Landau equation

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 2 • May 2017
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