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Contents of PMS, Vol. 40, Fasc. 2,
pages 269 - 295
DOI: 10.37190/0208-4147.40.2.5
Published online 9.7.2020
 

Weyl multifractional Ornstein--Uhlenbeck processes mixed with a Gamma distribution

Khalifa Es-Sebaiy
Fatima-Ezzahra Farah
Astrid Hilbert

Abstract: The aim of this paper is to study the asymptotic behavior of aggregated Weyl multifractional Ornstein–Uhlenbeck processes mixed with Gamma random variables. This allows us to introduce a new class of processes, Gamma-mixed Weyl multifractional Ornstein–Uhlenbeck processes (GWmOU), and study their elementary properties such as Hausdorff dimension, local self-similarity and short-range dependence. We also prove that these processes approach the multifractional Brownian motion.

2010 AMS Mathematics Subject Classification: Primary 60G22; Secondary 60G17.

Keywords and phrases: Weyl multifractional Ornstein--Uhlenbeck process, Gamma distribution, aggregated process, multifractional Brownian motion.

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