Incremental moments and Hölder exponents of multifractional multistable processes

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 Holder exponent is, as expected, related to the local stability index. We compute the precise value of the almost sure Holder exponent in the case of the multistable Levy motion, which turns out to reveal an interesting phenomenon.