On the fractional mixed fractional Brownian motion Time Changed by Inverse alpha Stable Subordinator

TL;DR

This paper investigates a time-changed fractional mixed fractional Brownian motion using an inverse alpha stable subordinator, demonstrating its long-range dependence properties under certain conditions.

Contribution

It introduces a new process combining fractional mixed fractional Brownian motion with an inverse alpha stable subordinator and proves its long-range dependence.

Findings

The process exhibits long-range dependence under specific conditions.

Long-range dependence holds for all H1 < H2.

The study extends understanding of time-changed stochastic processes.

Abstract

A time-changed fractional mixed fractional Brownian motion by inverse alpha stable subordinator with index alpha in (0, 1) is an iterated process L constructed as the superposition of fractional mixed fractional Brownian motion N(a, b) and an independent inverse {\alpha}-stable subordinator Talpha. In this paper we prove that the process LT alpha(a, b) is of long range dependence property under a smooth condition on the Hirsh index H1 and H2. We deduce that the fractional mixed fractional Brownian motion has long range dependence for every H1 < H2.