Journal article
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' decomposition for Brownian motion with drift. © Institute of Mathematical Statistics, 2005.
- Publication status:
- Published
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- Publisher copy:
- 10.1214/009117905000000422
Authors
- 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
- ARK identifier:
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- Copyright date:
- 2005
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