On strong law of large numbers for weakly stationary $φ$-mixing set-valued random variable sequences
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915848272216064 |
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| author | Tuyen, Luc Tri |
| author_facet | Tuyen, Luc Tri |
| contents | In this paper we extend the notion of $φ$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $φ$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On strong law of large numbers for weakly stationary $φ$-mixing set-valued random variable sequences Tuyen, Luc Tri Probability In this paper we extend the notion of $φ$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $φ$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp. |
| title | On strong law of large numbers for weakly stationary $φ$-mixing set-valued random variable sequences |
| topic | Probability |
| url | https://arxiv.org/abs/2601.09197 |