由 FBM 驱动的 McKean-Vlasov SDEs 的平均原理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-06 DOI:10.1007/s12346-024-01099-5

Tongqi Zhang, Yong Xu, Lifang Feng, Bin Pei

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引用次数: 0

摘要

本文研究了一类混合慢-快麦金-弗拉索夫随机微分方程，该方程包含具有赫斯特参数（H >1/2\）的分数布朗运动和标准布朗运动。首先，我们证明了混合耦合系统的存在性和唯一性定理。其次，在系数的适当假设下，利用哈明斯基时间离散化方法，我们证明慢速分量在均方意义上强烈收敛于相应平均方程的解。

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Averaging Principle for McKean-Vlasov SDEs Driven by FBMs

This paper considers a class of mixed slow-fast McKean–Vlasov stochastic differential equations that contain the fractional Brownian motion with Hurst parameter \(H > 1/2\) and the standard Brownian motion. Firstly, we prove an existence and uniqueness theorem for the mixed coupled system. Secondly, under suitable assumptions on the coefficients, using the approach of Khasminskii’s time discretization, we prove that the slow component strongly converges to the solution of the corresponding averaged equation in the mean square sense.

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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.

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