A0545
Title: Parameter estimation for a linear parabolic SPDE in two space dimensions with a small noise using spatiotemporal data
Authors: Yozo Tonaki - The University of Osaka (Japan)
Yusuke Kaino - Kobe University (Japan)
Masayuki Uchida - The University of Osaka (Japan) [presenting]
Abstract: The purpose is to study the estimation of unknown parameters in a second-order linear parabolic stochastic partial differential equation (SPDE) in two spatial dimensions, driven by a Q-Wiener process with a small noise, using high-frequency spatio-temporal observations. Previous works focused on minimum contrast estimators (MCEs) for unknown coefficients in a second-order linear parabolic SPDE in one space dimension driven by a cylindrical Wiener process based on high-frequency spatiotemporal data. Another study further developed parametric adaptive estimators for a second-order linear parabolic SPDE in one space dimension with small noise. The methodologies of prior studies are extended to a linear parabolic SPDE in two dimensions with a small noise, and MCEs are proposed for the diffusive and advective parameters using temporal and spatial increments. Furthermore, an estimator is introduced for the reaction parameter based on an approximate coordinate process. Simulation studies are presented to evaluate the performance of the proposed estimators.
