Open Access
Translator Disclaimer
November 2005 Growth of the Brownian forest
Jim Pitman, Matthias Winkel
Ann. Probab. 33(6): 2188-2211 (November 2005). DOI: 10.1214/009117905000000422


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.


Download Citation

Jim Pitman. Matthias Winkel. "Growth of the Brownian forest." Ann. Probab. 33 (6) 2188 - 2211, November 2005.


Published: November 2005
First available in Project Euclid: 7 December 2005

zbMATH: 1092.60033
MathSciNet: MR2184095
Digital Object Identifier: 10.1214/009117905000000422

Primary: 60J65 , 60J80

Keywords: binary Galton–Watson branching process , Brownian motion , Continuum random tree , forest-valued Markov process , Williams’ decomposition

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • November 2005
Back to Top