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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.

Occupation time problem for multifractional Brownian motion

Ouahra Mohamed Ait, Guerbaz Raby, Ouahhabi Hanae, Sghir Aissa

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 1

99--113

In this paper, by using a Fourier analytic approach, we investigate sample path properties of the fractional derivatives of multifractional Brownian motion local times. We also show that those additive functionals satisfy a property of local asymptotic self-similarity. As a consequence, we derive some local limit theorems for the occupation time of multifractional Brownian motion in the space of continuous functions.