OPTIMAL PARAMETER ESTIMATION FOR LINEAR SPDES FROM MULTIPLE MEASUREMENTS

• 成果类型: Article
• 署名作者: Altmeyer, Randolf; Tiepner, Anton; Wahl, Martin
• 署名单位: University of Cambridge; Aarhus University; University of Bielefeld
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2364
• 发表日期: 2024
• 页码: 1307-1333
• 关键词: time; RESOLUTION; transport; EQUATIONS; MODEL

摘要

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of measurements is nondecreasing, the rate of convergence for each coefficient depends on its differential order and is faster for higher order coefficients. Based on an explicit analysis of the reproducing kernel Hilbert space of a general stochastic evolution equation, a Gaussian lower bound scheme is introduced. As a result, minimax optimality of the rates as well as sufficient and necessary conditions for consistent estimation are established.