Incremental moments and H\"older exponents of multifractional multistable processes

TL;DR

This paper investigates the local structure of multifractional multistable processes, demonstrating how their incremental moments scale and how their pointwise exponents relate to localisability indices.

Contribution

It provides new results on the scaling behavior of incremental moments and the relationship between pointwise exponents and localisability indices for these processes.

Findings

Incremental moments exhibit specific scaling behavior.

Pointwise exponent is lower than the localisability index.

Results enhance understanding of local structure in 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 exponent is, as expected, lower than the localisability index.