Multi-mixed sub-fractional Brownian motion and Ornstein–Uhlenbeck processes
American institute of mathematical sciences
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©2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License.
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.
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2473-6988
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AIMS mathematics|11
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä (vertaisarvioitu)