Semiparametric estimation of McKean-Vlasov SDEs

被引：7

作者：

Belomestny, Denis ^{[1
,3
]}

Pilipauskaite, Vytaute ^{[2
]}

Podolskij, Mark ^{[2
]}

机构：

[1] Univ Duisburg Essen, Fac Math, Duisburg, Germany

[2] Univ Luxembourg, Dept Math, Esch sur Alzette, Luxembourg

[3] Natl Univ Higher Sch Econ, Moscow, Russia

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2023年 / 59卷 / 01期

基金：

欧洲研究理事会;

关键词：

Deconvolution; McKean-Vlasov SDEs; Mean field models; Multi-agent learning; Minimax bounds; Semiparametric estimation; GRANULAR MEDIA EQUATIONS;

D O I：

10.1214/22-AIHP1261

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：

In this paper we study the problem of semiparametric estimation for a class of McKean-Vlasov stochastic differential equations. Our aim is to estimate the drift coefficient of a MV-SDE based on observations of the corresponding particle system. We propose a semiparametric estimation procedure and derive the rates of convergence for the resulting estimator. We further prove that the obtained rates are essentially optimal in the minimax sense.

引用

页码：79 / 96

页数：18

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