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 $(y,t)$.
@article{1176990340,
author = {Chauvin, Brigitte},
title = {Product Martingales and Stopping Lines for Branching Brownian Motion},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 1195-1205},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990340}
}
Chauvin, Brigitte. Product Martingales and Stopping Lines for Branching Brownian Motion. Ann. Probab., Tome 19 (1991) no. 4, pp. 1195-1205. http://gdmltest.u-ga.fr/item/1176990340/