Limit theorems for critical branching processes in an extremely unfavorable random environment
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915696661757952 |
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| author | Vatutin, Vladimir Dyakonova, Elena |
| author_facet | Vatutin, Vladimir Dyakonova, Elena |
| contents | Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the domain of attraction of an $α$-stable law we prove conditional limit theorems describing, as $n\rightarrow \infty $, the distribution the number of particles in the process $\{Z_{m},0\leq m\leq n\}$ given $Z_{n}>0$ and $S_{n}\leq const$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit theorems for critical branching processes in an extremely unfavorable random environment Vatutin, Vladimir Dyakonova, Elena Probability 60G50 (Primary), 60J80, 60K37 (Secondary) Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the domain of attraction of an $α$-stable law we prove conditional limit theorems describing, as $n\rightarrow \infty $, the distribution the number of particles in the process $\{Z_{m},0\leq m\leq n\}$ given $Z_{n}>0$ and $S_{n}\leq const$. |
| title | Limit theorems for critical branching processes in an extremely unfavorable random environment |
| topic | Probability 60G50 (Primary), 60J80, 60K37 (Secondary) |
| url | https://arxiv.org/abs/2512.22592 |