Mixed Generalized Fractional Brownian Motion
Probability
2021-02-23 v1 Statistics Theory
Statistics Theory
Abstract
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well known mixed fractional Brownian motion introduced by Cheridito [10] and the generalized fractional Brownian motion introduced by Zili [31]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long range dependence properties of this process.
Keywords
Cite
@article{arxiv.2102.10166,
title = {Mixed Generalized Fractional Brownian Motion},
author = {Ezzedine Mliki and Shaykhah Alajmi},
journal= {arXiv preprint arXiv:2102.10166},
year = {2021}
}