Transformation of the discrete stable process via branching reproduction environment

Maroussia Slavtchova-Bojkova; Penka Mayster

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arXiv · 2503.23180

Transformation of the discrete stable process via branching reproduction environment

Maroussia Slavtchova-Bojkova·Penka Mayster

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Abstract

The current paper focuses on studying the impact of immigration with an infinite mean, driven by a discrete-stable compound Poisson process, when it is entering the branching environment with infinite variance of reproduction. Our goal is to determine the explicit form of the probability generating function and subsequently to analyze the probability of extinction, aiming to understand the long-term behavior of such processes.

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Maroussia Slavtchova-Bojkova, Penka Mayster. 2025-03-29. Transformation of the discrete stable process via branching reproduction environment. https://arxiv.org/abs/2503.23180

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