Splitting trees with neutral Poissonian mutations. II: Largest and oldest families

DOI10.1016/j.spa.2012.11.013zbMath1270.60090arXiv1108.4812OpenAlexW2038267394MaRDI QIDQ1939344

Nicolas Champagnat, Amaury Lambert

Publication date: 4 March 2013

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4812

zbMATH Keywords

extreme valuesbranching processLévy processscale functionCox processcoalescent point processallelic partitionCrump-Mode-Jagers processinfinite alleles modellinear birth-death processsplitting treemixed Poisson point process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Extreme value theory; extremal stochastic processes (60G70) Applications of branching processes (60J85) Markov renewal processes, semi-Markov processes (60K15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Genetics and epigenetics (92D10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (10)

Mutations on a random binary tree with measured boundary ⋮ Mutational pattern of a sample from a critical branching population ⋮ Central limit theorem for supercritical binary homogeneous Crump-Mode-Jagers processes ⋮ Birth and death processes with neutral mutations ⋮ Random ultrametric trees and applications ⋮ Approximation of the allelic frequency spectrum in general supercritical branching populations ⋮ Splitting Trees Stopped when the First Clock Rings and Vervaat's Transformation ⋮ Further properties of a random graph with duplications and deletions ⋮ Splitting trees with neutral mutations at birth ⋮ Splitting trees with neutral Poissonian mutations. I: Small families

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