Splitting trees stopped when the first clock rings and Vervaat's transformation

2011/10/13 by Amaury Lambert, Pieter Trapman, Lambert, Amaury +1
Agricultural and Biological Sciences · #60G17 #60G51 #60G55 #60J80 (Primary) 92D10 #60J85 #60K15 #60K25 (Secondary) #92D25 #92D30 #92D40 #FOS: Mathematics #Plant and Biological Electrophysiology Studies #Probability (math.PR)

paper · doi:10.48550/arxiv.1110.2929

openalex publication_date 2011/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a branching population where individuals have i.i.d. life lengths (not necessarily exponential) and constant birth rate. We let N_t denote the population size at time t. %(called homogeneous, binary Crump--Mode--Jagers process). We further assume that all individuals, at birth time, are equipped with independent exponential clocks with parameter δ. We are interested in the genealogical tree stopped at the first time T when one of those clocks rings. This question has applications in epidemiology, in population genetics, in ecology and in queuing theory. We show that conditional on \T

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