Growth of the Brownian forest
| dc.creator | Pitman, Jim | |
| dc.creator | Winkel, Matthias | |
| dc.date | 2004-04-09 | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T06:36:42Z | |
| dc.date.available | 2026-07-07T06:36:42Z | |
| dc.description | 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. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000422 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0404199 | |
| dc.identifier | http://arxiv.org/abs/math/0404199 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 6, 2188-2211 | |
| dc.identifier | doi:10.1214/009117905000000422 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100167 | |
| dc.subject | Probability | |
| dc.subject | 60J65, 60J80 (Primary) | |
| dc.title | Growth of the Brownian forest | |
| dc.type | text |