NONPARAMETRIC ESTIMATION FOR LINEAR SPDES FROM LOCAL MEASUREMENTS

• 成果类型: Article
• 署名作者: Altmeyer, Randolf; Reiss, Markus
• 署名单位: Humboldt University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1581
• 发表日期: 2021
• 页码: 1-38
• 关键词: infinite-dimensional parameter; identification

摘要

The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space. For the asymptotic regime with fixed time horizon and with the spatial resolution of the observations tending to zero, we provide rate-optimal estimators and establish scaling limits of the deterministic PDE and of the SPDE on growing domains. The estimators are robust to lower order perturbations of the underlying differential operator and achieve the parametric rate even in the nonparametric setup with a spatially varying coefficient. A numerical example illustrates the main results.