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Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes
Volume 10, Issue 4 (2023), pp. 343–366
Hamidreza Maleki Almani ORCID icon link to view author Hamidreza Maleki Almani details   Tommi Sottinen ORCID icon link to view author Tommi Sottinen details  

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https://doi.org/10.15559/23-VMSTA229
Pub. online: 26 June 2023      Type: Research Article      Open accessOpen Access

Received
29 January 2023
Revised
24 May 2023
Accepted
26 May 2023
Published
26 June 2023

Abstract

The so-called multi-mixed fractional Brownian motions (mmfBm) and multi-mixed fractional Ornstein–Uhlenbeck (mmfOU) processes are studied. These processes are constructed by mixing by superimposing or mixing (infinitely many) independent fractional Brownian motions (fBm) and fractional Ornstein–Uhlenbeck processes (fOU), respectively. Their existence as ${L^{2}}$ processes is proved, and their path properties, viz. long-range and short-range dependence, Hölder continuity, p-variation, and conditional full support, are studied.

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Keywords
Fractional Brownian motion Gaussian processes long-range dependence multi-mixed fractional Brownian motion multi-mixed fractional Ornstein–Uhlenbeck process short-range dependence stationary-increment processes stationary processes

MSC2010
60G10 60G15 60G22

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