乘法噪声驱动的慢-快 SPDE 平均原理中的最佳收敛速率

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics 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

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.