Estimation of the drift parameter for the fractional stochastic heat equation via power variation
Volume 6, Issue 4 (2019), pp. 397–417
Pub. online: 3 October 2019
Type: Research Article
Open Access
Open Access
Received
8 April 2019
8 April 2019
Revised
22 July 2019
22 July 2019
Accepted
11 September 2019
11 September 2019
Published
3 October 2019
3 October 2019
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.
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