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 in:Journal of dynamics and differential equations 2022-06, Vol.34 (2), p.1453-1487
Main Authors: Li, Dingshi, Wang, Bixiang, Wang, Xiaohu
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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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