PATH-VALUED BRANCHING PROCESSES AND NONLOCAL BRANCHING SUPERPROCESSES

• 成果类型: Article
• 署名作者: Li, Zenghu
• 署名单位: Beijing Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP759
• 发表日期: 2014
• 页码: 41-79
• 关键词: stochastic-equations; Levy processes; limit; FLOWS

摘要

A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time space noises. The family can be regarded as an inhomogeneous increasing path-valued branching process with immigration. Two nonlocal branching immigration superprocesses can be defined from the flow. We identify explicitly the branching and immigration mechanisms of those processes. The results provide new perspectives into the tree-valued Markov processes of Aldous and Pitman [Ann. Inst. Henri Poincare Probab. Stat. 34 (1998) 637-686] and Abraham and Delmas [Ann. Probab. 40 (2012) 1167-1211].