Growth of the Brownian forest
Jim Pitman and Matthias Winkel
Source: Ann. Probab. Volume 33, Number 6
(2005), 2188-2211.
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.
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Keywords: Continuum random tree; forest-valued Markov process; binary Galton–Watson branching process; Brownian motion; Williams’ decomposition
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1133965857
Digital Object Identifier: doi:10.1214/009117905000000422
Mathematical Reviews number (MathSciNet): MR2184095
Zentralblatt MATH identifier: 05020241
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