Strong law of large numbers for $φ$-sub-Gaussian random variables under sub-linear expectation spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911459215147008 |
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| author | Masasila, Nyanga Honda Fazekas, István |
| author_facet | Masasila, Nyanga Honda Fazekas, István |
| contents | We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the definition of the sub-Gaussian property into an upper part and a lower part. It turns out that this approach fits well to the sub-linear setting; it provides a proper framework for extending Zajkowski's general result to sublinear expectation spaces. Within our framework, we establish a strong law of large numbers for sub-Gaussian sequences. We present an example showing the usefulness of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong law of large numbers for $φ$-sub-Gaussian random variables under sub-linear expectation spaces Masasila, Nyanga Honda Fazekas, István Probability We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the definition of the sub-Gaussian property into an upper part and a lower part. It turns out that this approach fits well to the sub-linear setting; it provides a proper framework for extending Zajkowski's general result to sublinear expectation spaces. Within our framework, we establish a strong law of large numbers for sub-Gaussian sequences. We present an example showing the usefulness of our results. |
| title | Strong law of large numbers for $φ$-sub-Gaussian random variables under sub-linear expectation spaces |
| topic | Probability |
| url | https://arxiv.org/abs/2602.18175 |