@article{Shokrollahi2026, 
author = {Foad Shokrollahi and Tommi Sottinen and Mounir Zili},
title = {Multi-mixed sub-fractional Brownian motion and Ornstein–Uhlenbeck processes},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {3464-3498},
keywords = {conditional full support, Hölder continuity, mixed process, Ornstein-Uhlenbeck process, sub-fractional Brownian motion, mixed Gaussian processes},
url = {https://www.sciopen.com/article/10.3934/math.2026141},
doi = {10.3934/math.2026141},
abstract = {We proposed a novel class of Gaussian processes, the multi-mixed sub-fractional Brownian motion (mmsfBm) and its Ornstein-Uhlenbeck counterpart. The mmsfBm is an infinite linear combination of independent sub-fractional Brownian motions, a construction that enables it to capture a continuum of scaling properties and provides a significant mathematical advantage over finite-sum models. We rigorously proved that the local roughness of these processes is defined by the infimum of their Hurst exponents. We further showed that both processes are non-semimartingales and possess the conditional full support (CFS) property. The preservation of these unique regularity properties under the Ornstein-Uhlenbeck transformation is a key finding, confirming the robustness of this new framework for modeling complex, multi-scale systems in finance and other fields.}
}