Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes

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.

Keywords

• fractional Brownian motion
• Gaussian processes
• long-range dependence
• multi-mixed fractional Brownian motion
• multi-mixed fractional Ornstein–Uhlenbeck process
• short-range dependence