Adaptive estimator for a parabolic linear SPDE with a small noise

TL;DR

This paper proposes an adaptive estimation method for the coefficients of a parabolic linear SPDE with small noise, utilizing high-frequency data and data thinning techniques to improve estimation accuracy.

Contribution

It introduces a novel adaptive estimator for SPDE coefficients based on high-frequency data and data thinning, enhancing parameter estimation in small noise regimes.

Findings

Proposed estimators perform well in simulations.

Thinned data improves estimation accuracy.

Adaptive estimator effectively captures SPDE parameters.

Abstract

We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned data with respect to space obtained from the high frequency data, the minimum contrast estimators of two coefficient parameters of the SPDE are proposed. With these estimators and the thinned data with respect to time obtained from the high frequency data, we construct an approximation of the coordinate process of the SPDE. Using the approximate coordinate process, we obtain the adaptive estimator of a coefficient parameter of the SPDE. Moreover, we give simulation results of the proposed estimators of the SPDE.