Estimation for a linear parabolic SPDE in two space dimensions from discrete observations
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: IPS Abstract
Keywords: asymptotic_theory
Session: IPS 150 - Statistical inference for stochastic ordinary and partial differential equations
Monday 17 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
We consider parametric estimation of a parabolic linear second order stochastic partial differential equation (SPDE) with two-dimensional space based on high-frequency spatio-temporal data. The minimum contrast estimators (MCEs) of the diffusivity parameter and the curvature parameter in the SPDE are obtained by using thinned data in space. We derive the approximate coordinate process using the MCEs and the high-frequency spatio-temporal data. The adaptive estimators of coefficient parameters in the SPDE are constructed by using the MCEs and the thinned data in time obtained from the approximate coordinate process. It is shown that the adaptive estimators have consistency and asymptotic normality.