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Weyl Multifractional Ornstein-Uhlenbeck Processes Mixed with a Gamma Distribution

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FD2W02 - Fractional kinetics, hydrodynamic limits and fractals

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. Joint work with Kh. Es-Sebaiy, F.E. Farah e-publication, Probability and Mathematical Statistics, 40(2), 269-295 (2020). https://doi.org/10.37190/0208-4147.40.2.5

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