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

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.

Keywords

• stochastic heat equation
• fractional Brownian motion
• fractional Laplacian
• <italic>q</italic> variation
• drift parameter estimation