Growth of the Brownian forest

Jim Pitman, Matthias Winkel
2005 Annals of Probability  
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.
doi:10.1214/009117905000000422 fatcat:vsv5ub26qnfrnk5twua2cj3vsm