On the long range dependence of time-changed mixed fractional Brownian motion model

Ezzedine Mliki; Shaykhah Alajmi

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arXiv · 2102.10180

On the long range dependence of time-changed mixed fractional Brownian motion model

Ezzedine Mliki·Shaykhah Alajmi

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Abstract

A time-changed mixed fractional Brownian motion is an iterated process constructed as the superposition of mixed fractional Brownian motion and other process. In this paper we consider mixed fractional Brownian motion of parameters a, b and H\in(0, 1) time-changed by two processes, gamma and tempered stable subordinators. We present their main properties paying main attention to the long range dependence. We deduce that the fractional Brownian motion time-changed by gamma and tempered stable subordinators has long range dependence property for all H\in(0, 1).

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Ezzedine Mliki, Shaykhah Alajmi. 2021-02-19. On the long range dependence of time-changed mixed fractional Brownian motion model. https://arxiv.org/abs/2102.10180

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