An estimation of the stability and the localisability functions of multistable processes

Abstract

Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability functions, and we prove the consistency of those two estimators. We illustrate these convergences with two examples, the Lévy multistable process and the Linear Multifractional Multistable Motion.