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
收藏
页数：50
相关论文
共 50 条
  • [1] Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs
    Hong, Wei
    Li, Shihu
    Liu, Wei
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 316 : 94 - 135
  • [2] Lp-strong convergence of the averaging principle for slow-fast SPDEs with jumps
    Xu, Jie
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 445 (01) : 342 - 373
  • [3] Strong Averaging Principle for a Class of Slow-fast Singular SPDEs Driven by α-stable Process
    Xiaobin Sun
    Huilian Xia
    Yingchao Xie
    Xingcheng Zhou
    [J]. Frontiers of Mathematics, 2023, 18 : 565 - 590
  • [4] STRONG AVERAGING PRINCIPLE FOR SLOW-FAST SPDES WITH POISSON RANDOM MEASURES
    Xu, Jie
    Miao, Yu
    Liu, Jicheng
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (07): : 2233 - 2256
  • [5] Strong Averaging Principle for a Class of Slow-fast Singular SPDEs Driven by a-stable Process
    Sun, Xiaobin
    Xia, Huilian
    Xie, Yingchao
    Zhou, Xingcheng
    [J]. FRONTIERS OF MATHEMATICS, 2023, 18 (03): : 565 - 590
  • [6] Strong convergence of averaging principle for the non-autonomous slow-fast systems of SPDEs with polynomial growth
    Wang, Ruifang
    Xu, Yong
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (08) : 4665 - 4697
  • [7] On LP-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Levy noise
    Xu, Yong
    Yue, Hongge
    Wu, Jiang-Lun
    [J]. APPLIED MATHEMATICS LETTERS, 2021, 115
  • [8] Averaging principle for slow-fast stochastic Burgers equation driven by α-stable process
    Chen, Yalan
    Shi, Yinghui
    Sun, Xiaobin
    [J]. APPLIED MATHEMATICS LETTERS, 2020, 103
  • [9] Strong convergence rate of the averaging principle for a class of slow-fast stochastic evolution equations
    Xu, Jie
    Lian, Qiqi
    Liu, Jicheng
    [J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2023, 95 (04) : 581 - 614
  • [10] Noise-controlled dynamics through the averaging principle for stochastic slow-fast systems
    Wainrib, Gilles
    [J]. PHYSICAL REVIEW E, 2011, 84 (05):
12345