This work defines two classes of processes, that we term tempered fractional multistable motion and tempered multifractional stable motion. They are extensions of fractional multistable motion and multifractional stable motion, respectively, obtained by adding an exponential tempering to the integrands. We investigate certain basic features of these processes, including scaling property, tail probabilities, absolute moment, sample path properties, pointwise Hölder exponent, Hölder continuity of quasi norm, (strong) localisability and semi-long-range dependence structure. These processes may provide useful models for data that exhibit both dependence and varying local regularity/intensity of jumps.
Accepté le :
DOI : 10.1051/ps/2018012
Keywords: Stable processes, multistable processes, multifractional processes, sample paths, long-range dependence, localisability
Fan, Xiequan 1 ; Lévy Véhel, Jacques 1
@article{PS_2019__23__37_0,
author = {Fan, Xiequan and L\'evy V\'ehel, Jacques},
title = {Tempered fractional multistable motion and tempered multifractional stable motion},
journal = {ESAIM: Probability and Statistics},
pages = {37--67},
year = {2019},
publisher = {EDP Sciences},
volume = {23},
doi = {10.1051/ps/2018012},
mrnumber = {3921881},
zbl = {1411.60072},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2018012/}
}
TY - JOUR AU - Fan, Xiequan AU - Lévy Véhel, Jacques TI - Tempered fractional multistable motion and tempered multifractional stable motion JO - ESAIM: Probability and Statistics PY - 2019 SP - 37 EP - 67 VL - 23 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2018012/ DO - 10.1051/ps/2018012 LA - en ID - PS_2019__23__37_0 ER -
%0 Journal Article %A Fan, Xiequan %A Lévy Véhel, Jacques %T Tempered fractional multistable motion and tempered multifractional stable motion %J ESAIM: Probability and Statistics %D 2019 %P 37-67 %V 23 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2018012/ %R 10.1051/ps/2018012 %G en %F PS_2019__23__37_0
Fan, Xiequan; Lévy Véhel, Jacques. Tempered fractional multistable motion and tempered multifractional stable motion. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 37-67. doi: 10.1051/ps/2018012
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