Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes
Probability
2022-09-15 v2
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 processes and study their path properties, viz. long-range and short-range dependence, H\"older continuity, -variation, and conditional full support.
Keywords
Cite
@article{arxiv.2103.02978,
title = {Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes},
author = {Hamidreza Maleki Almani and Tommi Sottinen},
journal= {arXiv preprint arXiv:2103.02978},
year = {2022}
}