Diffusion approximation of critical controlled multi-type branching processes
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion approximation is derived for some critical CMBPs. Namely, we co...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
118 No. 3 |
| Tárgyszavak: | |
| doi: | 10.1007/s13398-024-01593-0 |
| mtmt: | 34918304 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/38040 |
| Tartalmi kivonat: | Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion approximation is derived for some critical CMBPs. Namely, we consider a sequence of appropriately scaled random step functions formed from a critical CMBP with control distributions having expectations that satisfy a kind of linearity assumption. It is proved that such a sequence converges weakly toward a squared Bessel process supported by a ray determined by an eigenvector of a matrix related to the offspring mean matrix and the control distributions of the branching process in question. As applications, among others, we derive Feller-type diffusion approximations of critical, primitive multi-type branching processes with immigration and some two-sex branching processes. We also describe the asymptotic behaviour of the relative frequencies of distinct types of individuals for critical CMBPs. |
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| Terjedelem/Fizikai jellemzők: | 36 |
| ISSN: | 1578-7303 |