On a class of critical Markov branching processes with non-homogeneous Poisson immigration
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910772478607360 |
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| author | Mitov, Kosto V. Yanev, Nikolay M. |
| author_facet | Mitov, Kosto V. Yanev, Nikolay M. |
| contents | The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that the mean number of immigrants is infinite and the intensity of the Poisson process converges to a constant. The asymptotic behavior of the probability for non-visiting zero is obtained. Proper limit distributions are proved, under suitable normalization of the sample paths, depending on the offspring distribution and the distribution of the immigrants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of critical Markov branching processes with non-homogeneous Poisson immigration Mitov, Kosto V. Yanev, Nikolay M. Probability The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that the mean number of immigrants is infinite and the intensity of the Poisson process converges to a constant. The asymptotic behavior of the probability for non-visiting zero is obtained. Proper limit distributions are proved, under suitable normalization of the sample paths, depending on the offspring distribution and the distribution of the immigrants. |
| title | On a class of critical Markov branching processes with non-homogeneous Poisson immigration |
| topic | Probability |
| url | https://arxiv.org/abs/2501.02277 |