
arXiv: 1611.01833
We consider a branching Brownian motion which starts from $0$ with drift $��\in \mathbb{R}$ and we focus on the number $Z_x$ of particles killed at $-x$, where $x>0$. Let us call $��_0$ the critical drift such that there is a positive probability of survival if and only if $��>-��_0$. Maillard \cite{maillard2013number} and Berestycki et al. \cite{berestycki2015branching} have study $Z_x$ in the case $��\leq -��_0$ and $��\geq ��_0$ respectively. We complete the picture by considering the case where $��>-��_0$ on the extinction event. More precisely we study the asymptotic of $q_i(x):=\mathbb{P}\left(Z_x=i,��_x��_c$.
32 pages, 1 figure
branching Brownian motion with absorption, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Branching processes (Galton-Watson, birth-and-death, etc.), Probability (math.PR), FOS: Mathematics, Continuous-time Markov processes on general state spaces, Mathematics - Probability, F-KPPs
branching Brownian motion with absorption, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Branching processes (Galton-Watson, birth-and-death, etc.), Probability (math.PR), FOS: Mathematics, Continuous-time Markov processes on general state spaces, Mathematics - Probability, F-KPPs
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