THE SURVIVAL PROBABILITY OF A CRITICAL MULTI-TYPE BRANCHING PROCESS IN IID RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Le Page, E.; Peigne, M.; Pham, C.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1243
• 发表日期: 2018
• 页码: 2946-2972
• 关键词: conditioned limit-theorems; PRODUCTS

摘要

We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type Galton-Watson process in i.i.d. random environments by using limit theorems for products of positive random matrices. Under suitable assumptions, the survival probability is proportional to 1/root n.