A LAMPERTI-TYPE REPRESENTATION OF CONTINUOUS-STATE BRANCHING PROCESSES WITH IMMIGRATION

• 成果类型: Article
• 署名作者: Emilia Caballero, M.; Perez Garmendia, Jose Luis; Uribe Bravo, Geronimo
• 署名单位: Universidad Nacional Autonoma de Mexico; Instituto Tecnologico Autonomo de Mexico; Universidad Nacional Autonoma de Mexico
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP766
• 发表日期: 2013
• 页码: 1585-1627
• 关键词: limit; time; CONVERGENCE; genealogy; EQUATIONS; profile; TREE

摘要

Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Levy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type previously studied by Grimvall, Kawazu and Watanabe and by Li) and a simulation scheme for continuous-state branching processes with immigration. We further apply our stability analysis to extend Pitman's limit theorem concerning Galton-Watson processes conditioned on total population size to more general offspring laws.