Theta-positive branching in varying environment
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912710802800640 |
|---|---|
| author | Sagitov, Serik Lindo, Alexey Zhumayev, Yerakhmet |
| author_facet | Sagitov, Serik Lindo, Alexey Zhumayev, Yerakhmet |
| contents | Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough investigation of such processes within a continuous-time framework, assuming that the reproduction law of individuals adheres to a specific parametric form for the probability generating function. Our six clear-cut limit theorems support the notion of recognizing five distinct asymptotical regimes for branching in varying environments: supercritical, asymptotically degenerate, critical, strictly subcritical, and loosely subcritical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04230 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theta-positive branching in varying environment Sagitov, Serik Lindo, Alexey Zhumayev, Yerakhmet Probability 60J80 Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough investigation of such processes within a continuous-time framework, assuming that the reproduction law of individuals adheres to a specific parametric form for the probability generating function. Our six clear-cut limit theorems support the notion of recognizing five distinct asymptotical regimes for branching in varying environments: supercritical, asymptotically degenerate, critical, strictly subcritical, and loosely subcritical. |
| title | Theta-positive branching in varying environment |
| topic | Probability 60J80 |
| url | https://arxiv.org/abs/2303.04230 |