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

共 50 条

[1] MCKEAN-VLASOV SDEs IN NONLINEAR FILTERING
Pathiraja, Sahani
Reich, Sebastian
Stannat, Wilhelm
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2021, 59 (06) : 4188 - 4215
[2] Importance sampling for McKean-Vlasov SDEs
dos Reis, Goncalo
Smith, Greig
Tankov, Peter
APPLIED MATHEMATICS AND COMPUTATION, 2023, 453
[3] Smoothing properties of McKean-Vlasov SDEs
Crisan, Dan
McMurray, Eamon
PROBABILITY THEORY AND RELATED FIELDS, 2018, 171 (1-2) : 97 - 148
[4] DERIVATIVE FORMULA FOR SINGULAR MCKEAN-VLASOV SDES
Wang, Feng-yu
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2023, 22 (06) : 1866 - 1898
[5] Derivative estimates on distributions of McKean-Vlasov SDEs
Huang, Xing
Wang, Feng-Yu
ELECTRONIC JOURNAL OF PROBABILITY, 2021, 26
[6] Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs
Amorino, Chiara
Belomestny, Denis
Pilipauskaite, Vytaute
Podolskij, Mark
Zhou, Shi-Yuan
PROBABILITY THEORY AND RELATED FIELDS, 2024,
[7] Weak Solutions of McKean-Vlasov SDEs with Supercritical Drifts
Zhang, Xicheng
COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2024, 12 (01) : 1 - 14
[8] Exponential convergence in entropy and Wasserstein for McKean-Vlasov SDEs
Ren, Panpan
Wang, Feng-Yu
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 206
[9] ITERATIVE MULTILEVEL PARTICLE APPROXIMATION FOR MCKEAN-VLASOV SDES
Szpruch, Lukasz
Tan, Shuren
Tse, Alvin
ANNALS OF APPLIED PROBABILITY, 2019, 29 (04): : 2230 - 2265
[10] Exponential ergodicity for singular reflecting McKean-Vlasov SDEs
Wang, Feng-Yu
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2023, 160 : 265 - 293

← 1 2 3 4 5 →