On a class of critical Markov branching processes with non-homogeneous Poisson immigration.
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| Title: | On a class of critical Markov branching processes with non-homogeneous Poisson immigration. |
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| Authors: | Mitov, Kosto V.1 (AUTHOR) kmitov@yahoo.com, Yanev, Nikolay M.2 (AUTHOR) |
| Source: | Stochastic Models. 2025, Vol. 41 Issue 4, p610-623. 14p. |
| Subjects: | Branching processes, Stochastic processes, Asymptotic distribution, Asymptotic expansions, Distribution (Probability theory) |
| Abstract: | The article 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | The article 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 15326349 |
| DOI: | 10.1080/15326349.2025.2492034 |
