Characterization of the finite variation property for a class of stationary increment infinitely divisible processes

TL;DR

This paper characterizes when certain stationary increment infinitely divisible processes have finite variation, providing zero-one laws and examples to clarify the conditions.

Contribution

It introduces new criteria and zero-one laws for the finite variation property in stationary increment infinitely divisible processes.

Findings

Zero-one laws for finite variation property

Criteria for finite variation in mixed moving averages

Examples illustrating the theoretical results

Abstract

We characterize the finite variation property for stationary increment mixed moving averages driven by infinitely divisible random measures. Such processes include fractional and moving average processes driven by Levy processes, and also their mixtures. We establish two types of zero-one laws for the finite variation property. We also consider some examples to illustrate our results.