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Modern Stochastics: Theory and Applications


Gamma mixed fractional Lévy Ornstein–Uhlenbeck process
Volume 11, Issue 1 (2024), pp. 63–83
Pub. online: 5 December 2023      Type: Research Article      Open accessOpen 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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© 2024 The Author(s). Published by VTeX
Open access article under the CC BY license.

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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