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.
Keywords: Hurst parameter estimation, wavelets, fractional Brownian motion, stochastic wave equation, Stein–Malliavin calculus, central limit theorem
@article{PS_2021__25_1_220_0,
author = {Assaad, Obayda and Tudor, Ciprian A.},
title = {Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space},
journal = {ESAIM: Probability and Statistics},
pages = {220--257},
year = {2021},
publisher = {EDP-Sciences},
volume = {25},
doi = {10.1051/ps/2021009},
mrnumber = {4265264},
zbl = {1478.60120},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2021009/}
}
TY - JOUR AU - Assaad, Obayda AU - Tudor, Ciprian A. TI - Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space JO - ESAIM: Probability and Statistics PY - 2021 SP - 220 EP - 257 VL - 25 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2021009/ DO - 10.1051/ps/2021009 LA - en ID - PS_2021__25_1_220_0 ER -
%0 Journal Article %A Assaad, Obayda %A Tudor, Ciprian A. %T Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space %J ESAIM: Probability and Statistics %D 2021 %P 220-257 %V 25 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2021009/ %R 10.1051/ps/2021009 %G en %F PS_2021__25_1_220_0
Assaad, Obayda; Tudor, Ciprian A. Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space. ESAIM: Probability and Statistics, Tome 25 (2021), pp. 220-257. doi: 10.1051/ps/2021009
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Supported by MATHAMSUD project SARC (19-MATH-06) and by Labex CEMPI (ANR-11-LABX-0007-01).
