乘法噪声驱动的慢-快 SPDE 平均原理中的最佳收敛速率

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-18 DOI:10.1007/s40304-023-00363-5

Yi Ge, Xiaobin Sun, Yingchao Xie

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引用次数: 0

摘要

本文研究了由乘法噪声驱动的慢-快随机偏微分方程的平均原理。在一些适当的条件下，利用泊松方程方法得到了收敛于相应平均方程解的慢分量的最佳阶数。更确切地说，强收敛和弱收敛的最优阶数分别为 1/2 和 1。值得指出的是，这里研究了两种强收敛，其中较强的一种回答了 Bréhier 在 [3, Remark 4.9] 中提出的一个开放问题。

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

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 Bréhier in [3, Remark 4.9].

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.