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February, 1993 On a First Passage Problem for Branching Brownian Motions
Ingemar Kaj, Paavo Salminen
Ann. Appl. Probab. 3(1): 173-185 (February, 1993). DOI: 10.1214/aoap/1177005513

Abstract

Consider a (space-time) realization ω of a critical or subcritical one-dimensional branching Brownian motion. Let Zx(ω) for x0 be the number of particles which are located for the first time on the vertical line through (x,0) and which do not have an ancestor on this line. In this note we study the process Z={Zx;x0}. We show that Z is a continuous-time Galton-Watson process and compute its creation rate and offspring distribution. Here we use ideas of Neveu, who considered a similar problem in a supercritical case. Moreover, in the critical case we characterize the continuous state branching processes obtained as weak limits of the processes Z under rescaling.

Citation

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Ingemar Kaj. Paavo Salminen. "On a First Passage Problem for Branching Brownian Motions." Ann. Appl. Probab. 3 (1) 173 - 185, February, 1993. https://doi.org/10.1214/aoap/1177005513

Information

Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60058
MathSciNet: MR1202521
Digital Object Identifier: 10.1214/aoap/1177005513

Subjects:
Primary: 60J65
Secondary: 60J80

Keywords: Branching Brownian motion , first passage , Galton-Watson process , Levy process , Super-Brownian motion , weak convergence

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 1 • February, 1993
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