CONSTRUCTION OF CONTINUOUS-STATE BRANCHING PROCESSES IN VARYING ENVIRONMENTS

• 成果类型: Article
• 署名作者: Fang, Rongjuan; Li, Zenghu
• 署名单位: Fujian Normal University; Beijing Normal University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1770
• 发表日期: 2022
• 页码: 3645-3673
• 关键词: exponential functionals; stochastic-equations; CONVERGENCE; REPRESENTATION; FLOWS; limit

摘要

A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven by time-space noises. The cumulant semigroup of the process is characterized in terms of a backward integral equation. We clarify the behavior of the process at its bottlenecks, which are the deterministic times when it arrives at zero almost surely by negative jumps. The process arises naturally as the scaling limit of Galton-Watson processes in varying environments.