POISSON EQUATION ON WASSERSTEIN SPACE AND DIFFUSION APPROXIMATIONS FOR MULTISCALE MCKEAN-VLASOV EQUATION

被引：2

作者：

Li, Yun ^{[1
]}

Wu, Fuke ^{[2
]}

Xie, Longjie ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221000, Jiangsu, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Poisson equation on Wasserstein space; diffusion approximation; McKean-Vlasov equation; multiscale processes; DISTRIBUTION DEPENDENT SDES; DIFFERENTIAL-EQUATIONS; CONVERGENCE; LIMIT;

D O I：

10.1137/22M1536856

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the Poisson equation on Wasserstein space, we derive the asymptotic limit as well as the quantitative error estimate of the convergence for the slow process. An extra homogenized drift term containing derivative in the measure argument of the solution of the Poisson equation appears in the limit, which seems to be new and is unique for systems involving the fast distribution.

引用

页码：1495 / 1524

页数：30

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