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 Δn → 0 and the number of particles N → ∞. Furthermore, we establish asymptotic normality under the additional constraint N Δn → 0, demonstrating that the underlying graphon structure can be rigorously handled despite the lack of identical distribution in the limit.
Related
- Drift parameter estimation for interacting particle systems with singular repulsion
- Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence
- Harmonizable Multifractional Stable Motion: estimators for the Hurst function and the stability parameter from discrete-time observations, their rates of convergence and the associated central limit theorems
- Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
- Parameter estimation in Conditional Sequential Monte Carlo algorithms through Particle Learning
BibTeX
@misc{amorino2026parameter,
title = {{Parameter estimation for graphon-interacting particle systems from discrete observations}},
author = {Chiara Amorino and Matteo Sfragara},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21710},
eprint = {2609.21710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21710},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parameter estimation for graphon-interacting particle systems from discrete observations
AU - Chiara Amorino
AU - Matteo Sfragara
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21710
UR - https://arxiv.org/abs/2609.21710
AB - 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 Δ_n → 0 and the number of particles N → ∞. Furthermore, we establish asymptotic normality under the additional constraint N Δ_n → 0, demonstrating that the underlying graphon structure can be rigorously handled despite the lack of identical distribution in the limit.
ER -