Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

TL;DR

This paper develops methods for estimating parameters of a two-dimensional linear parabolic SPDE using high-frequency spatial and temporal data, introducing novel estimators based on data thinning and approximation techniques.

Contribution

It introduces new estimation procedures for SPDE parameters leveraging high-frequency data and data thinning, with simulation validation.

Findings

Effective parameter estimators demonstrated through simulations.

Methodology accommodates high-frequency spatial and temporal data.

Provides a framework for practical SPDE parameter inference.

Abstract

We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types $Q$-Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the coordinate process of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose estimators of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results.