A Musielak-Orlicz approach for modeling uncertainties in long-memory processes

Hidekazu Yoshioka

doi:10.1016/j.chaos.2026.118494

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arXiv · 2604.00407

A Musielak-Orlicz approach for modeling uncertainties in long-memory processes

Hidekazu Yoshioka

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Abstract

This paper proposes a novel mathematical framework for modeling uncertainties in supOU processes, a common model for long-memory phenomena. We address uncertainties as distortions in reversion and Levy measures, evaluating them simultaneously via state-dependent divergence functions on Musielak-Orlicz spaces. The core of our approach involves solving optimization problems to determine the upper- and lower-bounds of cumulants under a prescribed uncertainty set. Notably, we demonstrate that while classical measures like Kullback-Leibler divergence fail in this context, Musielak-Orlicz spaces effectively resolve these issues. Along with providing sufficient conditions for the well-posedness of these optimizations, we demonstrate the framework's practical utility through a water environmental application, modeling streamflow discharge. This work offers both a theoretical advancement and a robust tool for long-memory process analysis.

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Hidekazu Yoshioka. 2026-04-01. A Musielak-Orlicz approach for modeling uncertainties in long-memory processes. https://doi.org/10.1016/j.chaos.2026.118494

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