Volume 17, 2013
|Page(s)||135 - 178|
|Published online||08 February 2013|
Incremental moments and Hölder exponents of multifractional multistable processes
UniversitéParis VI, Laboratoire de Probabilités et Modèles
Aléatoires 4 place Jussieu, 75252
Paris Cedex 05,
2 Regularity team, INRIA Saclay, Parc Orsay Université 4 rue Jacques Monod, Bat P, 91893 Orsay Cedex, France
Revised: 19 March 2011
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.
Mathematics Subject Classification: 60G17 / 60G18 / 60G22 / 60G52
Key words: Localisable processes / multistable processes / multifractional processes / pointwise Hölder regularity
© EDP Sciences, SMAI, 2013
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