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Weyl Multifractional Ornstein–Uhlenbeck Processes Mixed with A Gamma Distribution

Es-Sebaiy Khalifa, Farah Fatima-Ezzahra, Hilbert Astrid

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 2

269--295

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.