Rates on Yaglom's limit for Galton-Watson processes in a varying environment
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914962021023744 |
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| author | Cardona-Tobón, Natalia Jaramillo, Arturo Palau, Sandra |
| author_facet | Cardona-Tobón, Natalia Jaramillo, Arturo Palau, Sandra |
| contents | A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable normalization of the process conditioned on non-extinction converges in distribution to a standard exponential random variable. In this manuscript, we provide the rate of convergence of the Yaglom limit with respect to the Wasserstein metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11801 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rates on Yaglom's limit for Galton-Watson processes in a varying environment Cardona-Tobón, Natalia Jaramillo, Arturo Palau, Sandra Probability 60J80, 60F05, 60K37 A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable normalization of the process conditioned on non-extinction converges in distribution to a standard exponential random variable. In this manuscript, we provide the rate of convergence of the Yaglom limit with respect to the Wasserstein metric. |
| title | Rates on Yaglom's limit for Galton-Watson processes in a varying environment |
| topic | Probability 60J80, 60F05, 60K37 |
| url | https://arxiv.org/abs/2305.11801 |