Electronic Journal of Statistics

Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise

Marwa Khalil and Ciprian A. Tudor

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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.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 3639-3672.

Dates
Received: October 2017
First available in Project Euclid: 31 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1540951344

Digital Object Identifier
doi:10.1214/18-EJS1488

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60H05: Stochastic integrals 60G18: Self-similar processes

Keywords
Fractional Brownian motion stochastic wave equation quadratic variation Stein-Malliavin calculus central limit theorem almost sure central limit theorem Hurst parameter estimation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Khalil, Marwa; Tudor, Ciprian A. Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise. Electron. J. Statist. 12 (2018), no. 2, 3639--3672. doi:10.1214/18-EJS1488. https://projecteuclid.org/euclid.ejs/1540951344


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