Gamma mixed fractional Lévy Ornstein–Uhlenbeck process

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.

Keywords

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