Gamma mixed fractional Lévy Ornstein–Uhlenbeck process

Araya, Héctor; Garzón, Johanna; Rubilar-Torrealba, Rolando

doi:10.15559/23-VMSTA237

Modern Stochastics: Theory and Applications

Gamma mixed fractional Lévy Ornstein–Uhlenbeck process

Volume 11, Issue 1 (2024), pp. 63–83

Héctor Araya

Johanna Garzón Rolando Rubilar-Torrealba

https://doi.org/10.15559/23-VMSTA237

Pub. online: 5 December 2023 Type: Research Article

Open Access

Received
16 January 2023

Revised
14 September 2023

Accepted
12 November 2023

Published
5 December 2023

Abstract

In this article, a non-Gaussian long memory process is constructed by the aggregation of independent copies of a fractional Lévy 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.

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Keywords

Fractional Lévy process Ornstein–Uhlenbeck process non-Gaussian process random coefficients

MSC2010

60G10 60G17 60H05 60H30

Funding

Héctor Araya was partially supported by Proyecto Fondecyt 11230051, Proyecto ECOS210037 and Mathamsud AMSUD210023. Johanna Garzón was partially supported by HERMES project 58557 and Mathamsud AMSUD210023.

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