The survival probability of a critical multi-type branching process in i.i.d. random environment
| Autor: | C. Pham, E. Le Page, Marc Peigné |
|---|---|
| Přispěvatelé: | Peigné, Marc, Université de Bretagne Sud - Vannes (UBS Vannes), Université de Bretagne Sud (UBS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
prod
Statistics and Probability product of random matrices random environment AMS classification 60J80 60F17 60K37 [MATH] Mathematics [math] 01 natural sciences Combinatorics critical case 010104 statistics & probability Mathematics::Probability Joint probability distribution Applied mathematics [MATH]Mathematics [math] 0101 mathematics survival probability Mathematics Branching process 60J80 Cumulative distribution function 010102 general mathematics Moment-generating function Algebra of random variables Multi-type branching process 60K37 Random variate 60F17 Probability distribution Statistics Probability and Uncertainty Random variable |
| Zdroj: | Ann. Probab. 46, no. 5 (2018), 2946-2972 |
| ISSN: | 0091-1798 |
| DOI: | 10.1214/17-aop1243 |
| Popis: | Conditioned on the generating functions of offspring distribution, we study the asymp-totic behaviour of the probability of non-extinction of a critical multi-type Galton-Watson process in i.i.d. random environments by using limits theorems for products of positive random matrices. Under some certain assumptions, the survival probability is proportional to 1/ √ n. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|