Transformation of the discrete stable process via branching reproduction environment

2025/03/29 by Maroussia Slavtchova-Bojkova, Slavtchova-Bojkova, Maroussia, Penka Mayster +1
Mathematics · Medicine · #60J80 #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2503.23180

openalex publication_date 2025/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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