Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
30 January 2020 |
14 February 2020 |
10 March 2020 |
Abstract: We analyzed the generalized k-variations for the solution to the wave equation driven by an additive Gaussian noise which behaves as a fractional Brownian with Hurst parameter in time and is white in space. The k-variations are defined along filters of any order and of any length. We show that the sequence of generalized k-variation satisfies a Central Limit Theorem when and we estimate the rate of convergence for it via the Stein-Malliavin calculus. The results are applied to the estimation of the Hurst index. We construct several consistent estimators for HH and these estimators are analyzed theoretically and numerically.