An inhomogeneous controlled branching process
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909085446701056 |
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| author | González, Miguel Minuesa, Carmen Mota, Manuel del Puerto, Inés Ramos, Alfonso |
| author_facet | González, Miguel Minuesa, Carmen Mota, Manuel del Puerto, Inés Ramos, Alfonso |
| contents | A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the transition probabilities are non-stationary. Under not too restrictive hypotheses, this model presents the classical duality of branching processes: either becomes extinct almost surely or grows to infinity. Sufficient conditions for the almost sure extinction and for a positive probability of indefinite growth are provided. Finally rates of growth of the process provided the non-extinction are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An inhomogeneous controlled branching process González, Miguel Minuesa, Carmen Mota, Manuel del Puerto, Inés Ramos, Alfonso Probability A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the transition probabilities are non-stationary. Under not too restrictive hypotheses, this model presents the classical duality of branching processes: either becomes extinct almost surely or grows to infinity. Sufficient conditions for the almost sure extinction and for a positive probability of indefinite growth are provided. Finally rates of growth of the process provided the non-extinction are studied. |
| title | An inhomogeneous controlled branching process |
| topic | Probability |
| url | https://arxiv.org/abs/2401.16010 |