Estimation of the drift parameter for the fractional stochastic heat equation via power variation

TL;DR

This paper introduces power variation estimators for the drift parameter in a fractional stochastic heat equation, proving their consistency, asymptotic normality, and deriving convergence rates under the Wasserstein metric.

Contribution

It develops novel power variation estimators for the drift parameter in fractional stochastic heat equations with Gaussian noise, establishing their statistical properties.

Findings

Estimators are consistent and asymptotically normal.

Derived convergence rates under the Wasserstein metric.

Applicable to equations with white or correlated spatial noise.

Abstract

We define power variation estimators for the drift parameter of the stochastic heat equation with the fractional Laplacian and an additive Gaussian noise which is white in time and white or correlated in space. We prove that these estimators are consistent and asymptotically normal and we derive their rate of convergence under the Wasserstein metric.