A Musielak-Orlicz approach for modeling uncertainties in long-memory processes
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915997159522304 |
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| author | Yoshioka, Hidekazu |
| author_facet | Yoshioka, Hidekazu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Musielak-Orlicz approach for modeling uncertainties in long-memory processes Yoshioka, Hidekazu Optimization and Control Probability 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. |
| title | A Musielak-Orlicz approach for modeling uncertainties in long-memory processes |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2604.00407 |