Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-25T05:05:57.190Z Has data issue: false hasContentIssue false
  • English
  • Français

On Prolific Individuals in a Supercritical Continuous-State Branching Process

Part of: Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Jean Bertoin ,
Joaquin Fontbona  and
Servet Martínez
Jean Bertoin*
Affiliation:
Université Paris 6 and École Normale Supérieure
Joaquin Fontbona*
Affiliation:
Universidad de Chile
Servet Martínez*
Affiliation:
Universidad de Chile
*
∗Postal address: Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, 175 rue de Chevaleret, F-75013 Paris, France. Email address: [email protected]
∗∗Postal address: CMM-DIM, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
∗∗Postal address: CMM-DIM, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe the genealogy of individuals with infinite descent in a supercritical continuous-state branching process.

Keywords

Continuous-state branching processbranching mechanismextinctionreduced tree

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60E10: Characteristic functions; other transforms
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 714 - 726
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, Berlin.Google Scholar
[2] Bertoin, J. and Le Gall, J.-F. (2000). The Bolthausen–Sznitman coalescent and the genealogy of continuous-state branching processes. Prob. Theory Relat. Fields 117, 249–266.Google Scholar
[3] Duquesne, T. and Le Gall, J.-F. (2002). {Random trees, Lévy processes and spatial branching processes.} Astérisque 281, 147 pp.Google Scholar
[4] Duquesne, T. and Winkel, M. (2007). Growth of Lévy trees. Prob. Theory Relat. Fields 139, 313–371.CrossRefGoogle Scholar
[5] Grey, D. R. (1974). Asymptotic behaviour of continuous time continuous state-space branching processes. J. Appl. Prob. 11, 669–677.Google Scholar
[6] Kyprianou, A. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin.Google Scholar
[7] Lagerås, A. N. and Martin-Löf, A. (2006). Genealogy for supercritical branching processes. J. Appl. Prob. 43, 1066–1076.Google Scholar
[8] Le Gall, J.-F. (1999). Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhäuser, Basel.CrossRefGoogle Scholar
[9] Lyons, R. and Peres, Y. (2008). {Probability on trees and networks}. Available at http://mypage.iu.edu/∼ rdlyons/prbtree/book.pdf.Google Scholar
[10] Neveu, J. (1992). A continuous-state branching process in relation with the GREM model of spin glass theory. Res. Rep. 267, École Polytechnique.Google Scholar
[11] O'Connell, N. (1993). Yule process approximation for the skeleton of a branching process. J. Appl. Prob. 30, 725–729.Google Scholar
[12] Silverstein, M. L. (1968). A new approach to local times. J. Math. Mech. 17, 1023–1054.Google Scholar