A branching-selection process related to censored Galton–Walton processes

Olivier Couronné; Lucas Gerin

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 1, page 84-94
  • ISSN: 0246-0203

Abstract

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We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.

How to cite

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Couronné, Olivier, and Gerin, Lucas. "A branching-selection process related to censored Galton–Walton processes." Annales de l'I.H.P. Probabilités et statistiques 50.1 (2014): 84-94. <http://eudml.org/doc/272044>.

@article{Couronné2014,
abstract = {We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.},
author = {Couronné, Olivier, Gerin, Lucas},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Galton-Watson process; censored branching process; branching and selection},
language = {eng},
number = {1},
pages = {84-94},
publisher = {Gauthier-Villars},
title = {A branching-selection process related to censored Galton–Walton processes},
url = {http://eudml.org/doc/272044},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Couronné, Olivier
AU - Gerin, Lucas
TI - A branching-selection process related to censored Galton–Walton processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 1
SP - 84
EP - 94
AB - We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.
LA - eng
KW - Galton-Watson process; censored branching process; branching and selection
UR - http://eudml.org/doc/272044
ER -

References

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  1. [1] K. B. Athreya and P. E. Ney. Branching Processes. Dover Publications Inc., Mineola, NY, 2004. Zbl1070.60001MR2047480
  2. [2] J. Bérard and J.-B. Gouéré. Brunet–Derrida behavior of branching-selection particle systems on the line. Comm. Math. Phys.298 (2010) 323–342. Zbl1247.60124MR2669438
  3. [3] R. Durrett. Probability: Theory and Examples, 2nd edition. Duxbury Press, Belmont, CA, 1996. Zbl1202.60002MR1609153
  4. [4] V. V. Petrov. Sums of Independent Random Variables. Springer, New York, 1975. Zbl0322.60042MR388499
  5. [5] V. A. Topchiĭ. The time to extinction for Galton–Watson processes censored at a high level. Teor. Veroyatn. Primen.54 (2009) 271–287. Zbl1203.60133MR2761556
  6. [6] A. N. Zubkov. A degeneracy condition for a bounded branching process. Mat. Zametki8 (1970) 9–18. Zbl0232.60071MR267649

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