Abstract
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 $(y,t)$.
Citation
Brigitte Chauvin. "Product Martingales and Stopping Lines for Branching Brownian Motion." Ann. Probab. 19 (3) 1195 - 1205, July, 1991. https://doi.org/10.1214/aop/1176990340
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