Goodness-of-fit test for multistable Lévy processes

Abstract

The multistable processes are extensions of stable processes, where the index of stability is replaced by a function ranging in (0, 2). The aim of this article is to build a statistical test which is able to detect a multistable behavior of a process belonging to the class of the multistable Lévy processes. The properties are stated for a discrete observation scheme of one trajectory.