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2018 Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise
Marwa Khalil, Ciprian A. Tudor
Electron. J. Statist. 12(2): 3639-3672 (2018). DOI: 10.1214/18-EJS1488

Abstract

We compute the covariance function of the solution to the linear stochastic wave equation with fractional noise in time and white noise in space. We apply our findings to analyze the correlation structure of this Gaussian process and to study the asymptotic behavior in distribution of its spatial quadratic variation. As an application, we construct a consistent estimator for the Hurst parameter.

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Marwa Khalil. Ciprian A. Tudor. "Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise." Electron. J. Statist. 12 (2) 3639 - 3672, 2018. https://doi.org/10.1214/18-EJS1488

Information

Received: 1 October 2017; Published: 2018
First available in Project Euclid: 31 October 2018

zbMATH: 06970014
MathSciNet: MR3870508
Digital Object Identifier: 10.1214/18-EJS1488

Subjects:
Primary: 60G15
Secondary: 60G18, 60H05

JOURNAL ARTICLE
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Vol.12 • No. 2 • 2018
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