| Issue |
ESAIM: PS
Volume 25, 2021
|
|
|---|---|---|
| Page(s) | 220 - 257 | |
| DOI | https://doi.org/10.1051/ps/2021009 | |
| Published online | 28 May 2021 | |
Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space★
Université de Lille, CNRS, Laboratoire Paul Painlevé, UMR 8524,
59655
Villeneuve d’Ascq, France.
** Corresponding author: ciprian.tudor@univ-lille.fr
Received:
16
March
2020
Accepted:
3
May
2021
Via Malliavin calculus, we analyze the limit behavior in distribution of the spatial wavelet variation for the solution to the stochastic linear wave equation with fractional Gaussian noise in time and white noise in space. We propose a wavelet-type estimator for the Hurst parameter of the this solution and we study its asymptotic properties.
Mathematics Subject Classification: 60G15 / 60H05 / 60G18 / 60F12
Key words: Hurst parameter estimation / wavelets / fractional Brownian motion / stochastic wave equation / Stein–Malliavin calculus / central limit theorem
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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