A0344
Title: Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency spatio-temporal data
Authors: Yozo Tonaki - Osaka University (Japan)
Yusuke Kaino - Kobe University (Japan)
Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: The problem of estimating unknown coefficient parameters of linear parabolic second-order stochastic partial differential equations (SPDEs) is treated in two space dimensions driven by Q-Wiener processes using high-frequency spatiotemporal data. Recent studies investigated minimum contrast estimators (MCEs) for unknown coefficient parameters of a linear parabolic second-order SPDE in one space dimension driven by a cylindrical Wiener process based on high-frequency spatiotemporal data. The methodology of an existing study is applied to the SPDEs in two space dimensions, and MCEs of the coefficient parameters are introduced to the SPDEs in two space dimensions using temporal and spatial increments. The coordinate processes of the SPDEs are then approximated using the MCEs. Furthermore, utilizing the approximated coordinate processes, parametric adaptive estimators are proposed for the rest of the unknown parameters of the SPDEs. Numerical simulations of the proposed estimators are also provided.
