Limiting Behavior of Solutions to Mckean-Vlasov Fractional Sdes With HöLder Diffusion Coefficients

被引：0

作者：

Wang, Wenya ^{[1
]}

Guo, Zhongkai ^{[2
]}

Wang, Yanmin ^{[2
]}

机构：

[1] Jianghan Univ, Sch Artificial Intelligence, Wuhan, Peoples R China

[2] South Cent Minzu Univ, Sch Math & Stat, Wuhan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年

基金：

中国国家自然科学基金;

关键词：

averaging principle; distribution-dependent; Holder continuous diffusion; Yamada-Watanabe approximation; AVERAGING PRINCIPLE; DIFFERENTIAL-EQUATIONS; APPROXIMATIONS; SYSTEMS;

D O I：

10.1002/mma.10938

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the limiting behavior of solutions for a class of It & ocirc;-Doob fractional stochastic differential equations (SDEs) with distribution-dependent (McKean-Vlasov) and Holder diffusion coefficients, using the averaging principle. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel to suit the needs of this paper. Secondly, utilizing the Yamada-Watanabe approximation method and iterative techniques, we provide results on the existence and uniqueness of a strong solution to the equation. Finally, we discuss the convergence result in mean square sense between the solutions of the original equation and the averaged equation.

引用

页数：13

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