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

TL;DR

This paper studies the long-range dependence properties of a new class of stochastic processes called generalized mixed fractional Brownian motion, especially when time-changed by specific subordinators, revealing conditions for long-range dependence.

Contribution

It introduces the gmfBm and analyzes its long-range dependence under time change by tempered stable and Gamma subordinators, extending understanding of dependence in complex stochastic models.

Findings

Identifies conditions for long-range dependence in time-changed gmfBm.

Shows how different subordinators affect dependence properties.

Provides theoretical insights into the behavior of mixed fractional processes.

Abstract

We introduce a generalized mixed fractional Brownian motion (gmfBm) as a linear combination of two independent fractional Brownian motions with possibly different Hurst indices and investigate conditions under which the time-changed gmfBm exhibit long range dependence when the time-change is induced by a tempered stable subordinator or a Gamma process.