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

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.