Multistable processes, that is, processes which are, at each “time”, tangent to a stableprocess, but where the index of stability varies along the path, have been recentlyintroduced as models for phenomena where the intensity of jumps is non constant. In thiswork, we give further results on (multifractional) multistable processes related to theirlocal structure. We show that, under certain conditions, the incremental moments display ascaling behaviour, and that the pointwise Hölder exponent is, as expected, related to thelocal stability index. We compute the precise value of the almost sure Hölder exponent inthe case of the multistable Lévy motion, which turns out to reveal an interestingphenomenon.
