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:	https://explore.openaire.eu/search/publication?articleId=doi_________::8ef9bc1c96afe5445243ad940f0ebf3b https://doi.org/10.1016/j.spa.2021.05.001 Zobrazit plný text záznamu Full Text from ScienceDirect