In this work we characterize the local asymptotic self-similarity of harmonizable fractional Lévy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional Lévy motions.
Keywords: Local asymptotic self-similarity, harmonizable processes, fractional processes, spectral representations
@article{PS_2021__25_1_286_0,
author = {Basse-O{\textquoteright}Connor, Andreas and Gr{\o}nb{\ae}k, Thorbj{\o}rn and Podolskij, Mark},
title = {Local asymptotic self-similarity for heavy tailed harmonizable fractional {L\'evy} motions},
journal = {ESAIM: Probability and Statistics},
pages = {286--297},
year = {2021},
publisher = {EDP-Sciences},
volume = {25},
doi = {10.1051/ps/2021011},
mrnumber = {4281739},
zbl = {1478.60122},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2021011/}
}
TY - JOUR AU - Basse-O’Connor, Andreas AU - Grønbæk, Thorbjørn AU - Podolskij, Mark TI - Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions JO - ESAIM: Probability and Statistics PY - 2021 SP - 286 EP - 297 VL - 25 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2021011/ DO - 10.1051/ps/2021011 LA - en ID - PS_2021__25_1_286_0 ER -
%0 Journal Article %A Basse-O’Connor, Andreas %A Grønbæk, Thorbjørn %A Podolskij, Mark %T Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions %J ESAIM: Probability and Statistics %D 2021 %P 286-297 %V 25 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2021011/ %R 10.1051/ps/2021011 %G en %F PS_2021__25_1_286_0
Basse-O’Connor, Andreas; Grønbæk, Thorbjørn; Podolskij, Mark. Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions. ESAIM: Probability and Statistics, Tome 25 (2021), pp. 286-297. doi: 10.1051/ps/2021011
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