B0326
Title: Estimation for a linear parabolic SPDE in two space dimensions with a small noise based on high frequency data
Authors: Yozo Tonaki - Osaka University (Japan)
Yusuke Kaino - Kobe University (Japan)
Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: Parametric estimation is studied for a linear parabolic second-order stochastic partial differential equation (SPDE) with a small noise in two space dimensions driven by a Q-Wiener process from high-frequency spatio-temporal data. A prior study obtained minimum contrast estimators for unknown parameters of a linear parabolic second-order SPDE with a small noise in one space dimension driven by the cylindrical Wiener process based on high-frequency spatiotemporal data and proved the asymptotic normality of the estimators. Firstly, minimum contrast estimators are introduced for the three coefficient parameters of the SPDE with a small noise in two space dimensions driven by a Q-Wiener process using the thinned data with respect to spatial points. The coordinate process of the SPDE is then approximated utilizing the minimum contrast estimators. Note that this coordinate process is the Ornstein-Uhlenbeck process with a small noise. Lastly, parametric adaptive estimators for the rest of the unknown parameters of the SPDE are obtained by using the approximated coordinate process. Numerical simulations of the proposed estimators are also conducted.
