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A0328
Title: Estimation for a discretely observed linear parabolic SPDE in two space dimensions based on triple increments Authors:  Masayuki Uchida - Osaka University (Japan) [presenting]
Yozo Tonaki - Osaka University (Japan)
Yusuke Kaino - Kobe University (Japan)
Abstract: Parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) is addressed in two space dimensions using high-frequency spatio-temporal data. A driving process of the SPDE is assumed to be a Q-Wiener process. A prior study investigated parameter estimation of a linear parabolic second-order SPDE in one space dimension driven by a cylindrical Wiener process based on temporal and spatial increments (double increments) and proposed minimum contrast estimators (MCEs) with asymptotic normality. MCEs of the coefficient parameters of the SPDE are first introduced in two space dimensions based on temporal and two-dimensional spatial increments (triple increments) by applying the prior study's method to the SPDE in two space dimensions. Next, by using the MCEs, an approximate coordinate process of the SPDE is derived. Finally, parametric adaptive estimators of the coefficient parameters of the SPDE are proposed using the approximate coordinate process. Under certain regularity conditions, asymptotic normality of the adaptive estimators is shown. In addition, numerical simulations of the proposed estimators are presented.