arXiv:2409.02479 Abstract | arXiv Analytics

arXiv:2409.02479 [math.PR]Abstract References Reviews Resources

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

Published 2024-09-04Version 1

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.

Comments: 14 pages, 3 figures

Categories: math.PR

Subjects: 60J80, 60G70

Keywords: ergodic theorem, particles undergo brownian motions, study branching brownian motion, process converges, randomly shifted gumbel distribution

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