Gamma mixed fractional L\'evy Ornstein-Uhlenbeck process

TL;DR

This paper introduces a new non-Gaussian long memory process built from fractional Lévy Ornstein-Uhlenbeck processes, analyzing its properties, limit behavior, and providing simulations.

Contribution

It presents a novel long memory process constructed via aggregation of fractional Lévy Ornstein-Uhlenbeck processes with random coefficients, along with theoretical analysis and simulations.

Findings

Properties of the new process are characterized.

A limit theorem for the process is established.

Simulations illustrate the limit process behavior.

Abstract

In this article, we introduce a non Gaussian long memory process constructed by the aggregation of independent copies of a fractional L\'evy Ornstein-Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown.