%0 Journal Article %1 pw04 %A Pitman, Jim %A Winkel, Matthias %D 2005 %J Ann. Probab. %K Brownian_forest Brownian_tree Dept_Mathematics_Berkeley Dept_Statistics_Berkeley growth_process path_decomposition myown %N 6 %P 2188--2211 %R 10.1214/009117905000000422 %T Growth of the Brownian forest %U http://stat.berkeley.edu/users/pitman/brownian_forest.pdf %V 33 %X 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.

@article{pw04, abstract = {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.}, added-at = {2008-01-20T22:56:40.000+0100}, arxiv = {math.PR/0404199}, author = {Pitman, Jim and Winkel, Matthias}, biburl = {https://www.bibsonomy.org/bibtex/2fc30fe5d4c738cf37bd8f1d4a88778c8/pitman}, coden = {APBYAE}, doi = {10.1214/009117905000000422}, fjournal = {The Annals of Probability}, interhash = {4b9528b53f252eadf0f488d9327306c6}, intrahash = {fc30fe5d4c738cf37bd8f1d4a88778c8}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {Brownian_forest Brownian_tree Dept_Mathematics_Berkeley Dept_Statistics_Berkeley growth_process path_decomposition myown}, mrclass = {60J80 (60J65)}, mrnumber = {MR2184095 (2006j:60090)}, mrreviewer = {G{\"o}tz Kersting}, number = 6, pages = {2188--2211}, selected = {YES}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {Growth of the {B}rownian forest}, url = {http://stat.berkeley.edu/users/pitman/brownian_forest.pdf}, volume = 33, year = 2005 }