Power-fractional distributions and branching processes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915227472232448 |
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| author | Alsmeyer, Gerold Hoang, Viet Hung |
| author_facet | Alsmeyer, Gerold Hoang, Viet Hung |
| contents | In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this article, we explore a generalization of these distributions, first introduced by Sagitov and Lindo, which offers similar advantages. We refer to these as power-fractional distributions, primarily because, as we demonstrate, they exhibit power-law behavior. Along with a discussion of their additional properties, we present several results related to the Galton-Watson branching process in both constant and randomly varying environments, illustrating these advantages. The use of power-fractional distributions in continuous time, particularly within the framework of Markov branching processes, is also briefly addressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power-fractional distributions and branching processes Alsmeyer, Gerold Hoang, Viet Hung Probability Primary 60J80, Secondary 60K37, 60H25 In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this article, we explore a generalization of these distributions, first introduced by Sagitov and Lindo, which offers similar advantages. We refer to these as power-fractional distributions, primarily because, as we demonstrate, they exhibit power-law behavior. Along with a discussion of their additional properties, we present several results related to the Galton-Watson branching process in both constant and randomly varying environments, illustrating these advantages. The use of power-fractional distributions in continuous time, particularly within the framework of Markov branching processes, is also briefly addressed. |
| title | Power-fractional distributions and branching processes |
| topic | Probability Primary 60J80, Secondary 60K37, 60H25 |
| url | https://arxiv.org/abs/2503.18563 |