A0351
Title: Parametric estimation for discretely observed linear parabolic SPDEs in two space dimensions
Authors: Masayuki Uchida - Osaka University (Japan) [presenting]
Yozo Tonaki - Osaka University (Japan)
Yusuke Kaino - Kobe University (Japan)
Abstract: Estimating unknown coefficient parameters of linear parabolic second-order stochastic partial differential equations (SPDEs) in two space dimensions driven by Q-Wiener processes based on high-frequency data in time and space is considered. 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 from high-frequency data were studied previously by other researchers, who proved asymptotic normality of the MCEs. MCEs for unknown parameters of coordinate processes of the SPDEs in two space dimensions using thinned data with respect are obtained to space. By utilizing the MCEs, approximate coordinate processes of the SPDEs are constructed. Adaptive estimators are derived for the coefficient parameters of the SPDE using the approximate coordinate processes and thinned data concerning time. The adaptive estimators are proved to be asymptotically normal under some regular conditions. Simulation results of the proposed estimators are also presented.
