Limit theorems for weakly subcritical branching processes in random environment
| Autor: | Goetz Kersting, Valeriy Ivanovich Afanasyev, Vladimir Vatutin, Christian Boeinghoff |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
education.field_of_study General Mathematics 60J80 (Primary) 60G50 60F17 (Secondary) Population Probability (math.PR) Type (model theory) Random walk Branching (linguistics) Distribution (mathematics) Random environment FOS: Mathematics Limit (mathematics) Statistical physics Statistics Probability and Uncertainty education Mathematics - Probability Branching process Mathematics |
| DOI: | 10.48550/arxiv.1001.1672 |
| Popis: | For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, 'supercritical'. This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on non-extinction. Also a functional limit theorem is proven, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks. Comment: 35 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|