Title: Adaptive estimation of a parabolic SPDE with a small noise
Authors: Masayuki Uchida - Osaka University (Japan) [presenting]
Yusuke Kaino - Osaka University (Japan)
Abstract: Parametric estimation is considered for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency observations in time and space. Recently, the asymptotic normality of the minimum contrast estimators for the coefficient parameters of the discretely observed SPDE model on a fixed region has been shown. We first obtain the minimum contrast estimators of the diffusivity parameter and the curvature parameter in a parabolic linear SPDE with a small dispersion parameter by using the thinned data in space based on the high frequency observations. Next, the approximate coordinate process is derived from the minimum contrast estimators and the high frequency observations. The adaptive estimator of the remaining one unknown parameter in the SPDE with a small dispersion parameter is constructed by using the thinned data in time obtained from the approximate coordinate process. Moreover, we give some examples and simulation results of the estimators of the coefficient parameters in the SPDE with a small dispersion parameter.