A scaling limit theorem for controlled branching processes with a size-divisible term
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916913962024960 |
|---|---|
| author | González, Miguel Martín-Chávez, Pedro del Puerto, Inés |
| author_facet | González, Miguel Martín-Chávez, Pedro del Puerto, Inés |
| contents | We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a sum of an immigration size-dependent term and a size-divisible term. Our assumptions are established in terms of the probability generating functions of the offspring and control distributions, distinguishing in this latter case between the immigration and the size-divisible parts. The limit process is a continuous-state process with dependent immigration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A scaling limit theorem for controlled branching processes with a size-divisible term González, Miguel Martín-Chávez, Pedro del Puerto, Inés Probability 60J80, 60F05 We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a sum of an immigration size-dependent term and a size-divisible term. Our assumptions are established in terms of the probability generating functions of the offspring and control distributions, distinguishing in this latter case between the immigration and the size-divisible parts. The limit process is a continuous-state process with dependent immigration. |
| title | A scaling limit theorem for controlled branching processes with a size-divisible term |
| topic | Probability 60J80, 60F05 |
| url | https://arxiv.org/abs/2508.17116 |