具有完全依赖性的多尺度随机微分方程的强收敛性

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-09-12 DOI:10.1016/j.spl.2024.110271

Qing Ji, Jicheng Liu

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引用次数: 0

摘要

本文考虑了多尺度随机微分方程的强收敛问题，其中慢分量的扩散系数取决于快过程。我们提出了一个新的近似方程，并通过泊松方程技术证明了强收敛阶数为 1/2。我们提出了新的近似方程，并通过泊松方程技术证明了强收敛阶数为 1/2。特别是，当慢速分量的扩散系数不依赖于快速过程时，近似方程正是平均方程。这为我们研究具有完全依赖性的多尺度随机微分方程的强收敛性提供了一个新的视角。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strong convergence of multi-scale stochastic differential equations with a full dependence

This paper considers the strong convergence of multi-scale stochastic differential equations, where diffusion coefficient of the slow component depends on fast process. In this situation, it is well-known that strong convergence in the averaging principle does not hold in general.

We propose a new approximation equation, and prove that the order of strong convergence is

1 / 2

via the technique of Poisson equation. In particular, when diffusion coefficient of the slow component does not depend on fast process, the approximation equation is exactly the averaged equation. This provides us a new perspective to study the strong convergence of multi-scale stochastic differential equations with a full dependence.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.