Trimmed trees and embedded particle systems

• 成果类型: Article
• 署名作者: Fleischmann, K; Swart, JM
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000090
• 发表日期: 2004
• 页码: 2179-2221
• 关键词: branching-processes; exponential-growth; CONSTRUCTION; extinction

摘要

In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embedded binary branching particle systems.