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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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

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

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

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Digital Object Identifier

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

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

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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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