Studies on invariant measures of fractional stochastic delay Ginzburg-Landau equations on $ \mathbb{R}^n $

Abstract

This paper is concerned with invariant measures of fractional stochastic delay Ginzburg-Landau equations on the entire space $ \mathbb{R}^n $. We first derive the uniform estimates and the mean-square uniform smallness of the tails of solutions in corresponding space. Then we deduce the weak compactness of a set of probability distributions of the solutions applying the Ascoli-Arzel$ \grave{a} $. We finally prove the existence of invariant measures by applying Krylov-Bogolyubov's method.

Keywords

• stochastic delay equation
• unbounded domain
• fractional ginzburg-landau equation
• invariant measure