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arXiv · 2301.09751

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

Ezzedine Mliki
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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.

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Ezzedine Mliki. 2023-01-23. On the fractional mixed fractional Brownian motion Time Changed by Inverse alpha Stable Subordinator. https://arxiv.org/abs/2301.09751

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