Hermite Ornstein--Uhlenbeck processes mixed with a Gamma distribution

Soukaina Douissi                <meta name=

2020/96/1-2 (3) — DOI: 10.5486/PMD.2020.8443 — pp. 23-44

Hermite Ornstein—Uhlenbeck processes mixed with a Gamma distribution

Authors: Soukaina Douissi, Khalifa Es-Sebaiy and Ciprian A. Tudor

Abstract:

We construct a long-memory non-Gaussian stochastic process by aggregation, as limit of the empirical mean of identically distributed copies of Ornstein—Uhlenbeck processes with Hermite noise and random coefficients. We also study the asymptotic behavior of the process with respect to its parameter.

Keywords: Hermite processes, Gamma-distribution, long-range dependence, Langevin equation, fractional Brownian motion, Ornstein-Uhlenbeck process

Mathematics Subject Classification: 60F05, 60G15, 60H05, 60H07, 60F12