Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction

被引：0

作者：

Kolliopoulos, Nikolaos ^{[1
]}

Larsson, Martin ^{[2
]}

Zhang, Zeyu ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI USA

[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2025年 / 38卷 / 01期

基金：

美国国家科学基金会;

关键词：

Mean-field; Propagation of chaos; Order statistics; Extreme value theory; SDE; Interacting diffusions; LIMIT;

D O I：

10.1007/s10959-024-01397-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean-Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics.

引用

页数：22

共 19 条

[1]

[Anonymous], 2007, Springer Series in Operations Research and Financial Engineering

[2] Systemic Risk in Interbanking Networks [J].