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November, 1992 Decomposing the Branching Brownian Path
Kalvis M. Jansons, L. C. G. Rogers
Ann. Appl. Probab. 2(4): 973-986 (November, 1992). DOI: 10.1214/aoap/1177005584

Abstract

We consider a real-valued branching Brownian motion where particles are killed at rate $\mu$ and split at rate $\lambda \leq \mu$ into two independent offspring particles. The process dies out almost surely, so it reaches some lowest level. We prove a decomposition of the branching Brownian path at its minimum. The post-minimum path is just branching Brownian motion conditioned never to go beneath its initial point. The pre-minimum piece is independent of the post-minimum piece, and has the same law as the post-minimum piece reweighted by a functional of the endpoints of the tree. Applications to branching polymers are discussed.

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Kalvis M. Jansons. L. C. G. Rogers. "Decomposing the Branching Brownian Path." Ann. Appl. Probab. 2 (4) 973 - 986, November, 1992. https://doi.org/10.1214/aoap/1177005584

Information

Published: November, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60057
MathSciNet: MR1189426
Digital Object Identifier: 10.1214/aoap/1177005584

Subjects:
Primary: 60J65
Secondary: 60J70 , 60J85

Keywords: Branching Brownian motion , branching polymers , branching tree with heights , post-minimum , pre-minimum , rooted branching tree with heights , rooted family tree with heights , Super-Brownian motion , tree shape with heights

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.2 • No. 4 • November, 1992
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