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B0854
Title: Parametric inference for a parabolic SPDE from discrete observations Authors:  Masayuki Uchida - Osaka University (Japan) [presenting]
Yusuke Kaino - Osaka University (Japan)
Abstract: The focus is on the estimation problem of unknown parameters for a parabolic linear second order stochastic partial differential equation (SPDE) based on high-frequency data which are observed in time and space. Previously, the parabolic linear second order SPDE model based on high-frequency data observed on a fixed region has been studied. The asymptotic properties of least squares estimators has been proved for both the normalized volatility parameter and the curvature parameter. We propose adaptive maximum likelihood (ML) type estimators of the coefficient parameters including the volatility parameter of the parabolic linear second order SPDE model by using thinned data obtained from high-frequency data. It is also shown that the adaptive ML type estimators have asymptotic normality under some regularity conditions. Furthermore, in order to verify asymptotic performance of the adaptive ML type estimators of the coefficient parameters of the parabolic linear second order SPDE model based on high-frequency data, some examples and simulation results of the adaptive ML type estimators are given.