Branching processes in nearly degenerate varying environment
We investigate branching processes in varying environment, for which and , , where stands for the offspring mean in generation n . Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on nonextinction...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | JOURNAL OF APPLIED PROBABILITY
61 No. 4 |
| Tárgyszavak: | |
| doi: | 10.1017/jpr.2024.15 |
| mtmt: | 34848012 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37099 |
| Tartalmi kivonat: | We investigate branching processes in varying environment, for which and , , where stands for the offspring mean in generation n . Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on nonextinction, and adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting (2020). |
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| Terjedelem/Fizikai jellemzők: | 1107-1126 |
| ISSN: | 0021-9002 |