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

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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


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