Weyl Multifractional Ornstein-Uhlenbeck Processes Mixed with a Gamma Distribution

The aim of this paper is to study the asymptotic behavior of the aggregated Weyl multifractional Ornstein-Uhlenbeck processes mixed with Gamma random variables. This allows us to introduce a new process, so-called Gamma-mixed Weyl multifractional Ornstein-Uhlenbeck process (GWmOU), and study its elementary properties such as Hausdorff dimension, locally self-similarity and short range dependence. We also prove that the GWmOU process is a new candidate to approach the multifractional Brownian motion.
Epub 2020