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Estimation of the drift parameter for the fractional stochastic heat equation via power variation
Volume 6, Issue 4 (2019), pp. 397–417
Zeina Mahdi Khalil   Ciprian Tudor  

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https://doi.org/10.15559/19-VMSTA141
Pub. online: 3 October 2019      Type: Research Article      Open accessOpen Access

Received
8 April 2019
Revised
22 July 2019
Accepted
11 September 2019
Published
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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Keywords
Stochastic heat equation fractional Brownian motion fractional Laplacian q variation drift parameter estimation

MSC2010
60G15 60H05 60G18

Funding
C. Tudor is partially supported by Labex Cempi (ANR-11-LABX-0007-01) and MATHAMSUD Project SARC (19-MATH-06).

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