A0446
Title: Parametric estimation for a linear parabolic SPDE in two space dimensions under small diffusivity asymptotics
Authors: Yozo Tonaki - Osaka University (Japan) [presenting]
Yusuke Kaino - Kobe University (Japan)
Masayuki Uchida - Osaka University (Japan)
Abstract: Parametric estimation is considered for a second-order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a Q-Wiener process under small diffusivity asymptotics. An estimator of the reaction parameter is first provided in the linear parabolic SPDE in two space dimensions with small diffusive and advective parameters based on continuous spatiotemporal data applying the methodology of an existing study to the SPDE in two space dimensions. An estimator of the reaction parameter is then constructed based on high-frequency spatiotemporal data by discretizing the estimator based on the continuous data. Furthermore, it is shown that the estimators have consistency and asymptotic normality under certain asymptotic conditions, and the asymptotic properties of the estimator are verified based on high-frequency data by numerical simulations.
