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Growth of the Brownian forest

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' d...

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Publication status:
Published

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Publisher copy:
10.1214/009117905000000422

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Journal:
ANNALS OF PROBABILITY More from this journal
Volume:
33
Issue:
6
Pages:
2188-2211
Publication date:
2005-11-01
DOI:
ISSN:
0091-1798
Language:
English
Keywords:
Pubs id:
pubs:97549
UUID:
uuid:fd18c990-52ae-4c26-8d75-ed9f0a9cdd59
Local pid:
pubs:97549
Source identifiers:
97549
Deposit date:
2012-12-19

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