Work

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

Year: 2025

Type: article

Abstract: ABSTRACT In this paper, we investigate the limiting behavior of solutions for a class of Itô–Doob fractional stochastic differential equations (SDEs) with distribution‐dependent (McKean–Vlasov) and Hölder diffusion coefficients, using the averaging principle. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Grönwall 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.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10938

Authors: Wenya Wang, Zhongkai Guo, Yanmin Wang

Institutions: Jianghan University, South Central Minzu University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Award: G6157183707