Small positive values and limit theorems for supercritical branching processes with immigration in random environment
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929400940855296 |
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| author | Zhao, Yinxuan Zhang, Mei |
| author_facet | Zhao, Yinxuan Zhang, Mei |
| contents | Let $(Z_n)$ be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for $Z$ are investigated. Based on these results, the central limit theorem of $\log Z_n$ and the Edgeworth expansion are obtained. The study is taken under the assumption that each individual produces $0$ offspring with a positive probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small positive values and limit theorems for supercritical branching processes with immigration in random environment Zhao, Yinxuan Zhang, Mei Probability Let $(Z_n)$ be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for $Z$ are investigated. Based on these results, the central limit theorem of $\log Z_n$ and the Edgeworth expansion are obtained. The study is taken under the assumption that each individual produces $0$ offspring with a positive probability. |
| title | Small positive values and limit theorems for supercritical branching processes with immigration in random environment |
| topic | Probability |
| url | https://arxiv.org/abs/2402.15279 |