Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems

This paper deals with the limiting behavior of invariant measures of the stochastic delay lattice systems. Under certain conditions, we first show the existence of invariant measures of the systems and then establish the stability in distribution of the solutions. We finally prove that any limit poi...

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Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 34; no. 2; pp. 1453 - 1487
Main Authors Li, Dingshi, Wang, Bixiang, Wang, Xiaohu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2022
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Primary 37L55
60H10
Invariant measure
Stochastic lattice system
Stability in distribution
Secondary 34F05
37L30
Delay
Limit measure
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Summary:This paper deals with the limiting behavior of invariant measures of the stochastic delay lattice systems. Under certain conditions, we first show the existence of invariant measures of the systems and then establish the stability in distribution of the solutions. We finally prove that any limit point of a tight sequence of invariant measures of the stochastic delay lattice systems must be an invariant measure of the corresponding limiting system as the intensity of noise converges or the time-delay approaches zero. In particular, when the stochastic delay lattice systems are stable in distribution, we show the invariant measures of the perturbed systems converge to that of the limiting system.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-021-10011-7