English

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 L2L^2 processes and study their path properties, viz. long-range and short-range dependence, H\"older continuity, pp-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}
}