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.
@article{arxiv.2107.00539,
title = {Semiparametric estimation of McKean-Vlasov SDEs},
author = {Denis Belomestny and Vytautė Pilipauskaitė and Mark Podolskij},
journal= {arXiv preprint arXiv:2107.00539},
year = {2021}
}