Multistable processes, that is, processes which are, at each “time”, tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is non constant. In this work, we give further results on (multifractional) multistable processes related to their local structure. We show that, under certain conditions, the incremental moments display a scaling behaviour, and that the pointwise Hölder exponent is, as expected, related to the local stability index. We compute the precise value of the almost sure Hölder exponent in the case of the multistable Lévy motion, which turns out to reveal an interesting phenomenon.
Mots clés : localisable processes, multistable processes, multifractional processes, pointwise Hölder regularity
@article{PS_2013__17__135_0,
author = {Le Gu\'evel, Ronan and V\'ehel, Jacques L\'evy},
title = {Incremental moments and {H\"older} exponents of multifractional multistable processes},
journal = {ESAIM: Probability and Statistics},
pages = {135--178},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2011151},
mrnumber = {3021313},
zbl = {1292.60050},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2011151/}
}
TY - JOUR AU - Le Guével, Ronan AU - Véhel, Jacques Lévy TI - Incremental moments and Hölder exponents of multifractional multistable processes JO - ESAIM: Probability and Statistics PY - 2013 SP - 135 EP - 178 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011151/ DO - 10.1051/ps/2011151 LA - en ID - PS_2013__17__135_0 ER -
%0 Journal Article %A Le Guével, Ronan %A Véhel, Jacques Lévy %T Incremental moments and Hölder exponents of multifractional multistable processes %J ESAIM: Probability and Statistics %D 2013 %P 135-178 %V 17 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2011151/ %R 10.1051/ps/2011151 %G en %F PS_2013__17__135_0
Le Guével, Ronan; Véhel, Jacques Lévy. Incremental moments and Hölder exponents of multifractional multistable processes. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 135-178. doi : 10.1051/ps/2011151. http://www.numdam.org/articles/10.1051/ps/2011151/
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