Optimal Convergence Rates in the Averaging Principle for Slow-Fast SPDEs Driven by Multiplicative Noise

被引：1

作者：

Ge, Yi ^{[1
]}

Sun, Xiaobin ^{[2
]}

Xie, Yingchao ^{[2
]}

机构：

[1] Taizhou Univ, Dept Math, Taizhou 225300, Peoples R China

[2] Jiangsu Normal Univ, Res Inst Math Sci, Sch Math & Stat, Xuzhou 221116, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2024年

基金：

中国国家自然科学基金;

关键词：

Stochastic partial differential equations; Averaging principle; Slow-fast; Poisson equation; Strong and weak convergence rates; Multiplicative noise; REACTION-DIFFUSION EQUATIONS; DIFFERENTIAL-EQUATIONS; POISSON EQUATION; WEAK ORDER; APPROXIMATION; SYSTEMS;

D O I：

10.1007/s40304-023-00363-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the averaging principle is researched for slow-fast stochastic partial differential equations driven by multiplicative noises. The optimal orders for the slow component that converges to the solution of the corresponding averaged equation have been obtained by using the Poisson equation method under some appropriate conditions. More precisely, the optimal orders are 1/2 and 1 for the strong and weak convergences, respectively. It is worthy to point that two kinds of strong convergence are studied here and the stronger one of them answers an open question by Brehier in [3, Remark 4.9].

引用

页数：50

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