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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.17155 |
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| _version_ | 1866914574627766272 |
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| author | Shen, Yi Zhang, Zhenyuan |
| author_facet | Shen, Yi Zhang, Zhenyuan |
| contents | Shen and Zhang (2021) showed that almost periodicity naturally arises in the spectral representation of discrete-time $p$-adic self-similar processes with stationary increments. In this paper, we study several notions of almost periodicity as sample path properties of Banach space-valued $p$-adic sssi processes. We prove that Bohr almost periodicity is equivalent, as a path event, to continuity with respect to the $p$-adic topology. We also show that the corresponding equivalence fails for Weyl and Besicovitch almost periodicity. Finally, we extend the Bohr almost-periodic result to finite-dimensional random fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Almost periodicity as a path property for $p$-adic self-similar processes with stationary increments Shen, Yi Zhang, Zhenyuan Probability Shen and Zhang (2021) showed that almost periodicity naturally arises in the spectral representation of discrete-time $p$-adic self-similar processes with stationary increments. In this paper, we study several notions of almost periodicity as sample path properties of Banach space-valued $p$-adic sssi processes. We prove that Bohr almost periodicity is equivalent, as a path event, to continuity with respect to the $p$-adic topology. We also show that the corresponding equivalence fails for Weyl and Besicovitch almost periodicity. Finally, we extend the Bohr almost-periodic result to finite-dimensional random fields. |
| title | Almost periodicity as a path property for $p$-adic self-similar processes with stationary increments |
| topic | Probability |
| url | https://arxiv.org/abs/2605.17155 |