Research Communication | Open Access
Volume 2020 | Communication ID 165 |

Generalized k-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus

Meryem Slaoui
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.