Parameter estimation for graphon-interacting particle systems from discrete observations

Abstract

In this paper, we address the joint parameter estimation of drift and diffusion coefficients for heterogeneously interacting particle systems. Unlike the homogeneous setting, the interactions are governed by a graphon-weighted mean-field framework, which introduces significant analytical complexity: while homogeneous systems yield i.i.d. limits, our setting results in particles that are independent but non-identically distributed in the limit. Based on discrete observations of the system over a fixed time interval $[0,T]$, we propose a contrast function based on a pseudo-likelihood approach. We prove the consistency of the resulting estimators as the discretization step ${\Delta }_n\to 0$ and the number of particles $N\to \infty$. Furthermore, we establish asymptotic normality under the additional constraint $N{\Delta }_n\to 0$, demonstrating that the underlying graphon structure can be rigorously handled despite the lack of identical distribution in the limit.

arXiv comment43 pages