[en] In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean–Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval [0,T], we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step (Δn) and the number of particles ( N) satisfy Δn→0 and N→∞, and asymptotically normal when additionally the condition ΔnN→0 holds.
Disciplines :
Mathematics
Author, co-author :
AMORINO, Chiara ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
HEIDARI, Akram ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Pilipauskaitė, Vytautė; Department of Mathematical Sciences, Aalborg University, Denmark
PODOLSKIJ, Mark ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
yes
Language :
English
Title :
Parameter estimation of discretely observed interacting particle systems
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