Splitting Trees Stopped when the First Clock Rings and Vervaat's Transformation

DOI10.1239/jap/1363784434zbMath1277.60140arXiv1110.2929MaRDI QIDQ4918573

Amaury Lambert, Pieter Trapman

Publication date: 25 April 2013

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2929

zbMATH Keywords

samplingresolventbranching processLévy processscale functiondetectionepidemiologyprocessor sharingCrump-Mode-Jagers processsplitting treecontour processVervaat's transformationage and residual lifetimeundershoot and overshoot

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Epidemiology (92D30) Queueing theory (aspects of probability theory) (60K25) Applications of branching processes (60J85) Population dynamics (general) (92D25) Markov renewal processes, semi-Markov processes (60K15) Sample path properties (60G17) Ecology (92D40) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Genetics and epigenetics (92D10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Cites Work

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• Scaling limits via excursion theory: interplay between Crump-Mode-Jagers branching processes and processor-sharing queues
• Species abundance distributions in neutral models with immigration or mutation and general lifetimes
• Splitting trees with neutral Poissonian mutations. I: Small families
• A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection
• The M/G/1 processor-sharing model: Transient behavior
• Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval
• Splitting trees with neutral Poissonian mutations. II: Largest and oldest families
• The contour of splitting trees is a Lévy process
• Introductory lectures on fluctuations of Lévy processes with applications.
• The allelic partition for coalescent point processes
• On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes