• Bernoulli
  • Volume 23, Number 2 (2017), 1179-1201.

Irreducibility of stochastic real Ginzburg–Landau equation driven by $\alpha$-stable noises and applications

Ran Wang, Jie Xiong, and Lihu Xu

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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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Bernoulli, Volume 23, Number 2 (2017), 1179-1201.

Received: March 2015
Revised: August 2015
First available in Project Euclid: 4 February 2017

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$\alpha$-stable noises exponential ergodicity irreducibility moderate deviation principle stochastic real Ginzburg–Landau equation


Wang, Ran; Xiong, Jie; Xu, Lihu. Irreducibility of stochastic real Ginzburg–Landau equation driven by $\alpha$-stable noises and applications. Bernoulli 23 (2017), no. 2, 1179--1201. doi:10.3150/15-BEJ773.

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