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

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.

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.

DOI : 10.1214/12-AIHP504
Classification : 60J80
Mots clés : Galton-Watson process, censored branching process, branching and selection 
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Couronné, Olivier; Gerin, Lucas. A branching-selection process related to censored Galton-Walton processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 1, pp. 84-94. doi : 10.1214/12-AIHP504. http://www.numdam.org/articles/10.1214/12-AIHP504/

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

[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 | Zbl

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

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

[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 | Zbl

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

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