In this paper we are interested in multifractional stable processes where the self-similarity index H becomes time-dependent, while the stability index α remains constant. Using β- negative power variations ( − 1∕2 < β < 0), we propose estimators for the value at a fixed time of the multifractional function H which satisfies an η-Hölder condition and for α in two cases: multifractional Brownian motion (α = 2) and linear multifractional stable motion (0 < α < 2). We get the consistency of our estimates for the underlying processes together with the rate of convergence.
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DOI : 10.1051/ps/2019012
Keywords: Stable processes, multifractional processes, negative power variations, multifractional function
@article{PS_2020__24_1_1_0,
author = {Dang, Thi-To-Nhu},
title = {Estimation of the multifractional function and the stability index of linear multifractional stable processes},
journal = {ESAIM: Probability and Statistics},
pages = {1--20},
year = {2020},
publisher = {EDP Sciences},
volume = {24},
doi = {10.1051/ps/2019012},
mrnumber = {4052999},
zbl = {1447.60067},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2019012/}
}
TY - JOUR AU - Dang, Thi-To-Nhu TI - Estimation of the multifractional function and the stability index of linear multifractional stable processes JO - ESAIM: Probability and Statistics PY - 2020 SP - 1 EP - 20 VL - 24 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2019012/ DO - 10.1051/ps/2019012 LA - en ID - PS_2020__24_1_1_0 ER -
%0 Journal Article %A Dang, Thi-To-Nhu %T Estimation of the multifractional function and the stability index of linear multifractional stable processes %J ESAIM: Probability and Statistics %D 2020 %P 1-20 %V 24 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2019012/ %R 10.1051/ps/2019012 %G en %F PS_2020__24_1_1_0
Dang, Thi-To-Nhu. Estimation of the multifractional function and the stability index of linear multifractional stable processes. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 1-20. doi: 10.1051/ps/2019012
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