Galton-Watson processes in dynamical environments
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913563657895936 |
|---|---|
| author | Morand, Thomas |
| author_facet | Morand, Thomas |
| contents | We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We study the extinction probability q in the uniformly supercritical case. In particular, we investigate the regularity of this application as a function of the environment x. In the critical case, we study the set of bad environments N (where the probability of extinction is one), which is T -invariant. We give its Hausdorff dimension in some cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galton-Watson processes in dynamical environments Morand, Thomas Dynamical Systems Probability We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We study the extinction probability q in the uniformly supercritical case. In particular, we investigate the regularity of this application as a function of the environment x. In the critical case, we study the set of bad environments N (where the probability of extinction is one), which is T -invariant. We give its Hausdorff dimension in some cases. |
| title | Galton-Watson processes in dynamical environments |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2410.19327 |