The Brownian net

• 成果类型: Article
• 署名作者: Sun, Rongfeng; Swart, Jan M.
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP357
• 发表日期: 2008
• 页码: 1153-1208
• 关键词: web

摘要

The (standard) Brownian web is a collection of coalescing one-dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.