Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case - Institut Camille Jordan Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case

Xinxin Chen
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Résumé

The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time $0$. The particle moves according to a Brownian motion with drift $\mu = 2$ and diffusion coefficient $\sigma^2 = 2$, until an independent exponential time of parameter $1$. At that time, the particle dies giving birth to two children who then start independent copies of the same process from their birth place. It is well-known that in this system, the cloud of particles eventually drifts to $\infty$. The aim of this note is to provide a precise estimate for the total number of particles that were born on the negative half-line, investigating in particular the tail decay of this random variable.
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Dates et versions

hal-03251329 , version 1 (26-01-2022)
hal-03251329 , version 2 (17-11-2022)

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Xinxin Chen, Bastien Mallein. Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case. 2022. ⟨hal-03251329v1⟩
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