Multi-Mixed Fractional Brownian Motions and Orstein-Uhlenbeck Processes

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 $L^2$ processes and study their path properties, viz. long-range and short-range dependence, H"older continuity, $p$-variation, and conditional full support.