English

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}
}
R2 v1 2026-06-23T23:20:33.012Z