Almost sure, L1- and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration
Under a first order moment condition on the immigration mechanism, we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration (CBI process) converges almost surely. If an x log(x) moment condition on the branc...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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2020
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| Sorozat: | SCIENCE CHINA MATHEMATICS
63 No. 10 |
| Tárgyszavak: | |
| doi: | 10.1007/s11425-019-1552-1 |
| mtmt: | 31487259 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/39620 |
| Tartalmi kivonat: | Under a first order moment condition on the immigration mechanism, we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration (CBI process) converges almost surely. If an x log(x) moment condition on the branching mechanism does not hold, then the limit is zero. If this x log(x) moment condition holds, then we prove L-1 convergence as well. The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing. If, in addition, a suitable extra power moment condition on the branching mechanism holds, then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L-1 limit. Moreover, under a second order moment condition on the branching and immigration mechanisms, we prove L-2 convergence of an appropriately scaled process and the above-mentioned projections as well. A representation of the limits is also provided under the same moment conditions. |
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| Terjedelem/Fizikai jellemzők: | 2089-2116 |
| ISSN: | 1674-7283 |