Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes
Volume 10, Issue 4 (2023), pp. 343–366
Pub. online: 26 June 2023
Type: Research Article
Open Access
Open Access
Received
29 January 2023
29 January 2023
Revised
24 May 2023
24 May 2023
Accepted
26 May 2023
26 May 2023
Published
26 June 2023
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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