Parameter estimation of discretely observed interacting particle systems

Asymptotic normality; Consistency; Interacting particle systems; McKean–Vlasov equation; Nonlinear diffusion; Parameter estimation; Discrete observations; Interacting particle system; Interacting particles; Joint parameter estimations; McKean-Vlasov equations; Parameters estimation; Stochastics; Statistics and Probability; Modeling and Simulation; Applied Mathematics; Nonlinear; diffusion

Abstract :

[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

Publication date :

September 2023

Journal title :

Stochastic Processes and Their Applications

ISSN :

0304-4149

eISSN :

1879-209X

Publisher :

Elsevier B.V.

Volume :

163

Pages :

350 - 386

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0304414923001321?httpAccept=text/xml

European Projects :

H2020 - 815703 - STAMFORD - Statistical Methods For High Dimensional Diffusions

Name of the research project :

Statistical Methods For High Dimensional Diffusions

Funders :

European Research Council
Union Européenne

Funding number :

815703

Funding text :

The authors gratefully acknowledge financial support of ERC Consolidator Grant 815703 “STAMFORD: Statistical Methods for High Dimensional Diffusions”.

Available on ORBilu :

since 28 November 2023

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