A simple backward construction of Branching Brownian motion with large displacement and applications

Julien Berestycki; Éric Brunet; Aser Cortines; Bastien Mallein

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arXiv · 1810.05809

A simple backward construction of Branching Brownian motion with large displacement and applications

Julien Berestycki·Éric Brunet·Aser Cortines·Bastien Mallein

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Abstract

In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal processes of several branching processes, including branching Brownian motions with variable speed and multitype branching Brownian motions. We give a new, alternative representation of these point measures and we show that they form a continuous family. This also yields a simple probabilistic expression for the constant that appears in the large deviation probability of having a large displacement. As an application, we show that Bovier and Hartung (2015)'s results about variable speed branching Brownian motion also describe the extremal point process of branching Ornstein-Uhlenbeck processes.

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Julien Berestycki, Éric Brunet, Aser Cortines, Bastien Mallein. 2018-10-13. A simple backward construction of Branching Brownian motion with large displacement and applications. https://arxiv.org/abs/1810.05809

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