Functional limit theorem for branching processes in nearly degenerate varying environment
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929615368355840 |
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| author | Kevei, Peter Kubatovics, Kata |
| author_facet | Kevei, Peter Kubatovics, Kata |
| contents | We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or add inhomogeneous immigration. Extending our one-dimensional limit results we derive functional limit theorems. In the former case, the limiting process is a time-changed simple birth-and-death process on $(-\infty, 0]$ conditioned on survival at $0$, while in the latter, it is a time-changed stationary continuous time branching process with immigration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional limit theorem for branching processes in nearly degenerate varying environment Kevei, Peter Kubatovics, Kata Probability 60J80, 60F05 We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or add inhomogeneous immigration. Extending our one-dimensional limit results we derive functional limit theorems. In the former case, the limiting process is a time-changed simple birth-and-death process on $(-\infty, 0]$ conditioned on survival at $0$, while in the latter, it is a time-changed stationary continuous time branching process with immigration. |
| title | Functional limit theorem for branching processes in nearly degenerate varying environment |
| topic | Probability 60J80, 60F05 |
| url | https://arxiv.org/abs/2412.03325 |