Finite Variation of Fractional Levy Processes

TL;DR

This paper characterizes when fractional Levy processes have finite variation, providing criteria based on the Levy process's characteristics and sample path properties, along with a zero-one law and an expected variation formula.

Contribution

It introduces new criteria for finite variation in fractional Levy processes, linking path differentiability and Levy triplet conditions, and presents a zero-one law and expected variation formula.

Findings

Finite variation characterized by Levy triplet and path differentiability.

Zero-one law established for finite variation property.

Formula derived for expected total variation.

Abstract

Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of the sample paths. A zero-one law and a formula for the expected total variation is also given.