Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes

Hamidreza Maleki Almani; Tommi Sottinen

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arXiv · 2103.02978

Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes

Hamidreza Maleki Almani·Tommi Sottinen

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Abstract

We study the so-called multi-mixed fractional Brownian motions (mmfBm) and multi-mixed fractional Ornstein--Ulhenbeck (mmfOU) processes. These processes are constructed by mixing by superimposing (infinitely many) independent fractional Brownian motions (fBm) and fractional Ornstein--Uhlenbeck processes (fOU), respectively. We prove their existence as $L^2$ processes and study their path properties, viz. long-range and short-range dependence, H\"older continuity, $p$-variation, and conditional full support.

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BibTeX RIS

Hamidreza Maleki Almani, Tommi Sottinen. 2021-03-04. Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes. https://arxiv.org/abs/2103.02978

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