Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise

Xintao Li; Xintao Li

doi:10.3934/math.2022425

AIMS Mathematics

2022, Volume 7, Issue 5: 7569-7594. doi: 10.3934/math.2022425

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Research article

Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise

Xintao Li ^,

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received: 04 November 2021 Revised: 18 January 2022 Accepted: 24 January 2022 Published: 15 February 2022
MSC : 37L30, 37L55, 37L60

In this article, we investigate the Wong-Zakai approximations of a class of second order non-autonomous stochastic lattice systems with additive white noise. We first prove the existence and uniqueness of tempered pullback random attractors for the original stochastic system and its Wong-Zakai approximation. Then, we establish the upper semicontinuity of these attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.
- Wong-Zakai approximation,
- lattice systems,
- random attractor,
- white noise,
- upper semicontinuity
Citation: Xintao Li. Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise[J]. AIMS Mathematics, 2022, 7(5): 7569-7594. doi: 10.3934/math.2022425

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Abstract

In this article, we investigate the Wong-Zakai approximations of a class of second order non-autonomous stochastic lattice systems with additive white noise. We first prove the existence and uniqueness of tempered pullback random attractors for the original stochastic system and its Wong-Zakai approximation. Then, we establish the upper semicontinuity of these attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.

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