A branching-selection process related to censored Galton-Walton processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 1, p. 84-94

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.

Nous étudions un cas particulier de système de particules avec branchement et sélection introduit par Bérard et Gouéré [Comm. Math. Phys. 298 (2010) 323-342]. Nous obtenons l'asympotique pour la vitesse, en remarquant un lien avec un processus de Galton-Watson surcritique censuré à un certain niveau.

DOI : https://doi.org/10.1214/12-AIHP504
Classification:  60J80
Keywords: Galton-Watson process, censored branching process, branching and selection
@article{AIHPB_2014__50_1_84_0,
     author = {Couronn\'e, Olivier and Gerin, Lucas},
     title = {A branching-selection process related to censored Galton-Walton processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {1},
     year = {2014},
     pages = {84-94},
     doi = {10.1214/12-AIHP504},
     zbl = {1286.60085},
     mrnumber = {3161523},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_1_84_0}
}
Couronné, Olivier; Gerin, Lucas. A branching-selection process related to censored Galton-Walton processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 1, pp. 84-94. doi : 10.1214/12-AIHP504. http://www.numdam.org/item/AIHPB_2014__50_1_84_0/

[1] K. B. Athreya and P. E. Ney. Branching Processes. Dover Publications Inc., Mineola, NY, 2004. | MR 2047480 | Zbl 1070.60001

[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. | MR 2669438 | Zbl 1247.60124

[3] R. Durrett. Probability: Theory and Examples, 2nd edition. Duxbury Press, Belmont, CA, 1996. | MR 1609153 | Zbl 1202.60002

[4] V. V. Petrov. Sums of Independent Random Variables. Springer, New York, 1975. | MR 388499 | Zbl 0322.60042

[5] V. A. Topchiĭ. The time to extinction for Galton-Watson processes censored at a high level. Teor. Veroyatn. Primen. 54 (2009) 271-287. | MR 2761556 | Zbl 1203.60133

[6] A. N. Zubkov. A degeneracy condition for a bounded branching process. Mat. Zametki 8 (1970) 9-18. | MR 267649 | Zbl 0232.60071