On a class of critical Markov branching processes with non-homogeneous Poisson immigration

Kosto V. Mitov; Nikolay M. Yanev

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arXiv · 2501.02277

On a class of critical Markov branching processes with non-homogeneous Poisson immigration

Kosto V. Mitov·Nikolay M. Yanev

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Abstract

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.

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Kosto V. Mitov, Nikolay M. Yanev. 2025-01-04. On a class of critical Markov branching processes with non-homogeneous Poisson immigration. https://arxiv.org/abs/2501.02277

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