The extremal process of branching Brownian motion with absorption

In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions with drift and are killed upon reaching the origin. We prove that the extremal process of this branching Brownian motion with absorption converges to a random shifted decorated Poisson point process. Furthermore, we show that the law of the right-most particle converges to the law of a random shifted Gumbel random variable.
Comment: 23 pages