## Bernoulli

- 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

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

Received: March 2015

Revised: August 2015

First available in Project Euclid: 4 February 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1486177396

**Digital Object Identifier**

doi:10.3150/15-BEJ773

**Mathematical Reviews number (MathSciNet)**

MR3606763

**Zentralblatt MATH identifier**

06701623

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.bj/1486177396