Averaging Principle for McKean-Vlasov SDEs Driven by FBMs

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

引用次数: 0

Abstract

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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由 FBM 驱动的 McKean-Vlasov SDEs 的平均原理

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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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

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