Complete left tail asymptotic for supercritical multitype branching processes
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915377913528320 |
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| author | Kutsenko, Anton A. |
| author_facet | Kutsenko, Anton A. |
| contents | We derive a complete left-tail asymptotic series for the density of the {\it martingale limit} of a supercritical multitype Galton-Watson process in the Schröder case. We show that the series converges everywhere, not only for small arguments. This is the first complete result regarding the left tails of multitype branching processes. A good, quickly computed approximation for the density will also be derived from the series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete left tail asymptotic for supercritical multitype branching processes Kutsenko, Anton A. Probability Functional Analysis We derive a complete left-tail asymptotic series for the density of the {\it martingale limit} of a supercritical multitype Galton-Watson process in the Schröder case. We show that the series converges everywhere, not only for small arguments. This is the first complete result regarding the left tails of multitype branching processes. A good, quickly computed approximation for the density will also be derived from the series. |
| title | Complete left tail asymptotic for supercritical multitype branching processes |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2507.06209 |