Asymptotics of nearly critical Galton-Watson processes with immigration
We investigate the inhomogeneous Galton-Watson processes with immigration, where pn, the offspring means in the nt h generation, tends to 1. We show that if the second derivatives of the offspring generating functions go to 0 rapidly enough, then the asymptotics are the same as in the INAR(l) case,...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2011
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| Sorozat: | Acta scientiarum mathematicarum
77 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16413 |
| Tartalmi kivonat: | We investigate the inhomogeneous Galton-Watson processes with immigration, where pn, the offspring means in the nt h generation, tends to 1. We show that if the second derivatives of the offspring generating functions go to 0 rapidly enough, then the asymptotics are the same as in the INAR(l) case, treated in [4]. We also determine the limit if this assumption does not hold showing the optimality of the conditions. |
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| Terjedelem/Fizikai jellemzők: | 681-702 |
| ISSN: | 0001-6969 |