Growth of the Brownian forest

• 成果类型: Article
• 署名作者: Pitman, J; Winkel, M
• 署名单位: University of California System; University of California Berkeley; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000422
• 发表日期: 2005
• 页码: 2188-2211
• 关键词: path decomposition; fluctuation identities

摘要

Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton-Watson forests with i.i.d. exponential branch lengths. We give elementary proofs of this composition rule and explain how it is intimately linked with Williams' decomposition for Brownian motion with drift.