图论相互作用粒子系统离散观测下的参数估计
Parameter estimation for graphon-interacting particle systems from discrete observations
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中文总结 AI 辅助
本文针对图论加权平均场框架下异质粒子系统，提出基于伪似然的对比函数，在离散观测下联合估计漂移和扩散系数，证明估计量的一致性和渐近正态性。
中文摘要 AI 辅助
本文研究了异质相互作用粒子系统中漂移和扩散系数的联合参数估计问题。与同质设置不同，相互作用由图论加权平均场框架控制，这引入了显著的分析复杂性：同质系统产生独立同分布极限，而我们的设置导致粒子在极限中独立但非同分布。基于系统在固定时间区间$[0, T]$上的离散观测，我们提出了一种基于伪似然方法的对比函数。我们证明了当离散化步长$\Delta_n \to 0$且粒子数$N \to \infty$时，所得估计量的一致性。此外，在额外约束$N \Delta_n \to 0$下，我们建立了渐近正态性，表明尽管极限中缺乏同分布性，潜在的图论结构可以被严格处理。
英文摘要
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 $Δ_n \to 0$ and the number of particles $N \to \infty$. Furthermore, we establish asymptotic normality under the additional constraint $N Δ_n \to 0$, demonstrating that the underlying graphon structure can be rigorously handled despite the lack of identical distribution in the limit.
发表机构
- Universitat Pompeu Fabra（庞佩法布拉大学）
- Barcelona School of Economics（巴塞罗那经济学院）
- University of Padova（帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。
