A critical branching process with immigration in random environment
| Autor: | Valeriy Ivanovich Afanasyev |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables Sequence Applied Mathematics Process (computing) Random walk Lévy process Distribution (mathematics) Mathematics::Probability Modeling and Simulation Limit (mathematics) Statistical physics Branching process Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 139:110-138 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2021.05.001 |
| Popis: | A Galton–Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is normalized by a random coefficient depending on the random environment only. The distribution of the limiting process is described in terms of a strictly stable Levy process and a sequence of independent and identically distributed random variables which is independent of this process. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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