Addendum to: Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914448947544064 |
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| author | Bürger, Reinhard |
| author_facet | Bürger, Reinhard |
| contents | In this addendum we extend Theorem 4.6 on the negative binomial distribution in `Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics' (Journal of Mathematical Biology 92:40, 2026; arXiv:2503.21403). We prove that the fractional linear lower bound to the negative binomial generating function derived there is indeed valid for every $x\in[0,1]$, and not only for $x\in[0,P^\infty_{\rm NB}]$, where $P^\infty_{\rm NB}$ is the extinction probability of the associated Galton-Watson process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Addendum to: Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics Bürger, Reinhard Probability 60J80 (Primary) 92D10, 92D15, 60J85 (Secondary) In this addendum we extend Theorem 4.6 on the negative binomial distribution in `Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics' (Journal of Mathematical Biology 92:40, 2026; arXiv:2503.21403). We prove that the fractional linear lower bound to the negative binomial generating function derived there is indeed valid for every $x\in[0,1]$, and not only for $x\in[0,P^\infty_{\rm NB}]$, where $P^\infty_{\rm NB}$ is the extinction probability of the associated Galton-Watson process. |
| title | Addendum to: Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics |
| topic | Probability 60J80 (Primary) 92D10, 92D15, 60J85 (Secondary) |
| url | https://arxiv.org/abs/2604.04848 |