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July, 1991 Product Martingales and Stopping Lines for Branching Brownian Motion
Brigitte Chauvin
Ann. Probab. 19(3): 1195-1205 (July, 1991). DOI: 10.1214/aop/1176990340


For a branching Brownian motion, a probability space of trees is defined. By analogy with stopping times on $\mathbb{R}$, stopping lines are defined to get a general branching property. We exhibit an intrinsic class of martingales which are products indexed by the elements of a stopping line. We prove that all these martingales have the same limit which we identify. Two particular cases arise: the line of particles living at time $t$ and the first crossings of a straight line whose equation is $y = at - x$ in the plane $(y,t)$.


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Brigitte Chauvin. "Product Martingales and Stopping Lines for Branching Brownian Motion." Ann. Probab. 19 (3) 1195 - 1205, July, 1991.


Published: July, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0738.60079
MathSciNet: MR1112412
Digital Object Identifier: 10.1214/aop/1176990340

Primary: 60J60
Secondary: 60G40 , 60G44 , 60J80

Keywords: Branching Brownian motion , stopping line

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 3 • July, 1991
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