Incremental moments and Hölder exponents of multifractional multistable processes

Ronan Le Guével; Jacques Lévy Véhel

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 135-178
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Le Guével, Ronan, and Véhel, Jacques Lévy. "Incremental moments and Hölder exponents of multifractional multistable processes." ESAIM: Probability and Statistics 17 (2013): 135-178. <http://eudml.org/doc/274390>.

@article{LeGuével2013,
abstract = {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.},
author = {Le Guével, Ronan, Véhel, Jacques Lévy},
journal = {ESAIM: Probability and Statistics},
keywords = {localisable processes; multistable processes; multifractional processes; pointwise Hölder regularity},
language = {eng},
pages = {135-178},
publisher = {EDP-Sciences},
title = {Incremental moments and Hölder exponents of multifractional multistable processes},
url = {http://eudml.org/doc/274390},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 135
EP - 178
AB - 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.
LA - eng
KW - localisable processes; multistable processes; multifractional processes; pointwise Hölder regularity
UR - http://eudml.org/doc/274390
ER -

References

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