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