B0526
Title: Estimation for linear parabolic SPDEs in two space dimensions based on high-frequency data
Authors: Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: Parametric estimation is addressed for linear parabolic second-order stochastic partial differential equations (SPDEs) in two space dimensions driven by Q-Wiener processes from high-frequency data in time and space. Minimum contrast estimators have been proposed for unknown parameters of the SPDE in one space dimension driven by the cylindrical Wiener process from high-frequency data and showed the asymptotic normality of the estimators. We first derive minimum contrast estimators for unknown parameters of the coordinate processes of the SPDEs in two space dimensions from the thinned data with respect to space. Next, we deduce approximate coordinate processes of the SPDEs in two space dimensions using the minimum contrast estimators. Finally, we obtain adaptive estimators of the coefficient parameters of the SPDEs in two space dimensions using the approximate coordinate processes from the thinned data with respect to time. It is proved that the adaptive estimators have asymptotic normality under some regularity conditions. Numerical simulations of the proposed estimators are also performed.
