An ergodic theorem for the maximum of branching Brownian motion with absorption

2024/09/04 by Yang, Fan
#FOS: Mathematics #Primary: 60J80 #Probability (math.PR) #Secondary: 60G70

paper · doi:10.48550/arxiv.2409.02479

Abstract

In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this process converges almost surely to a randomly shifted Gumbel distribution.

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