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.
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页码：79 / 96
页数：18
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