On the Besov-Orlicz path regularity of some Gaussian processes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913102595883008 |
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| author | Belfadli, Rachid Boufoussi, Brahim Ouknine, Youssef |
| author_facet | Belfadli, Rachid Boufoussi, Brahim Ouknine, Youssef |
| contents | In this paper, we rely on the additive decomposition in law satisfied by a class of stochastic processes, combined with the well-known regulariy properties of fractional Brownian motion, to establish Besov-Orlicz regularity of their sample paths. This provides a unified and direct proof for a broad class of processes, including bifractional Brownian motion with parameters $H\in (0, 1]$, $ K\in (0, 2)$ such that $HK \in (0, 1)$, subfractional Brownian motion with Hurst parameter $H\in (0, 1)$, and certain class of self-similar processes. %associated with the stochastic heat equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07571 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Besov-Orlicz path regularity of some Gaussian processes Belfadli, Rachid Boufoussi, Brahim Ouknine, Youssef Probability Primary 60H15, 60G18, Secondary 60G17, 46E35 In this paper, we rely on the additive decomposition in law satisfied by a class of stochastic processes, combined with the well-known regulariy properties of fractional Brownian motion, to establish Besov-Orlicz regularity of their sample paths. This provides a unified and direct proof for a broad class of processes, including bifractional Brownian motion with parameters $H\in (0, 1]$, $ K\in (0, 2)$ such that $HK \in (0, 1)$, subfractional Brownian motion with Hurst parameter $H\in (0, 1)$, and certain class of self-similar processes. %associated with the stochastic heat equation. |
| title | On the Besov-Orlicz path regularity of some Gaussian processes |
| topic | Probability Primary 60H15, 60G18, Secondary 60G17, 46E35 |
| url | https://arxiv.org/abs/2605.07571 |