Ray-Knight representation of flows of branching processes with competition by pruning of Levy trees

• 成果类型: Article
• 署名作者: Berestycki, J.; Fittipaldi, M. C.; Fontbona, J.
• 署名单位: University of Oxford; Universidad Nacional Autonoma de Mexico; Universidad de Chile; Universidad de Chile
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0819-4
• 发表日期: 2018
• 页码: 725-788
• 关键词: stochastic-equations; diffusion

摘要

We introduce flows of branching processes with competition, which describe the evolution of general continuous state branching populations in which interactions between individuals give rise to a negative density dependence term. This generalizes the logistic branching processes studied by Lambert (Ann Appl Probab 15(2):1506-1535, 2005). Following the approach developed by Dawson and Li (Ann Probab 40(2):813-857, 2012), we first construct such processes as the solutions of certain flow of stochastic differential equations. We then propose a novel genealogical description for branching processes with competition based on interactive pruning of Levy-trees, and establish a Ray-Knight representation result for these processes in terms of the local times of suitably pruned forests.