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Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Dingshi Li

  2. Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA

    Bixiang Wang

  3. Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

    Xiaohu Wang

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  1. Dingshi Li
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  2. Bixiang Wang
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  3. Xiaohu Wang
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Correspondence to Xiaohu Wang.

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This work was supported by NSFC (11871049, 11971394 and 12090013), Sichuan Science and Technology Program (2019YJ0215) and Foundation of Sichuan University (2020SCUNL111).

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Li, D., Wang, B. & Wang, X. Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems. J Dyn Diff Equat 34, 1453–1487 (2022). https://doi.org/10.1007/s10884-021-10011-7

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  • DOI: https://doi.org/10.1007/s10884-021-10011-7

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