Mixed Generalized Fractional Brownian Motion

TL;DR

This paper introduces a new Gaussian process called mixed generalized fractional Brownian motion, generalizing existing models and analyzing its stochastic properties, dependence structure, and non-semimartingale conditions.

Contribution

It proposes a novel mixed Gaussian process that extends known models and explores its key stochastic and dependence properties.

Findings

The process exhibits long-range dependence.

It is generally non-Markovian and non-stationary.

Conditions for non-semimartingale behavior are identified.

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.