Growth of the Brownian forest

Details Growth of the Brownian forest Growth of the Brownian forest

2004-04-09

arxiv.org/abs/math/0404199v2

Annals of Probability 2005, Vol. 33, No. 6, 2188-2211

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000422 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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.

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