由 FBM 驱动的 McKean-Vlasov SDEs 的平均原理

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems 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。

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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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

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.