# 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

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topLe 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 -

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