Open AccessLimiting behavior of invariant measures of highly nonlinear stochastic retarded lattice systems
Author(s) -
Yusen Lin,
Dingshi Li
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022054
Subject(s) - invariant measure , limiting , invariant (physics) , nonlinear system , mathematics , lattice (music) , homogeneous , statistical physics , mathematical analysis , pure mathematics , physics , mathematical physics , combinatorics , quantum mechanics , mechanical engineering , acoustics , engineering , ergodic theory
This paper deals with the limiting behavior of invariant measures of the highly nonlinear stochastic retarded lattice systems. Although invariant measures of stochastic retarded lattice system has been studied recently, there is so far no result of invariant measure of stochastic retarded lattice systems with highly nonlinear drift or diffusion terms. We first show the existence of invariant measures of the systems. We then prove that any limit point of a tight sequence of invariant measures of the stochastic retarded lattice systems must be an invariant measure of the corresponding limiting system as the intensity of noise converges or the time-delay approaches zero.