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.
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}, pages = {84--94}, publisher = {Gauthier-Villars}, volume = {50}, number = {1}, year = {2014}, doi = {10.1214/12-AIHP504}, mrnumber = {3161523}, zbl = {1286.60085}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/12-AIHP504/} }
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 SP - 84 EP - 94 VL - 50 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/12-AIHP504/ DO - 10.1214/12-AIHP504 LA - en ID - AIHPB_2014__50_1_84_0 ER -
%0 Journal Article %A Couronné, Olivier %A Gerin, Lucas %T A branching-selection process related to censored Galton-Walton processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2014 %P 84-94 %V 50 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/12-AIHP504/ %R 10.1214/12-AIHP504 %G en %F 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://archive.numdam.org/articles/10.1214/12-AIHP504/
[1] Branching Processes. Dover Publications Inc., Mineola, NY, 2004. | MR | Zbl
and .[2] Brunet-Derrida behavior of branching-selection particle systems on the line. Comm. Math. Phys. 298 (2010) 323-342. | MR | Zbl
and .[3] Probability: Theory and Examples, 2nd edition. Duxbury Press, Belmont, CA, 1996. | MR | Zbl
.[4] Sums of Independent Random Variables. Springer, New York, 1975. | MR | Zbl
.[5] The time to extinction for Galton-Watson processes censored at a high level. Teor. Veroyatn. Primen. 54 (2009) 271-287. | MR | Zbl
.[6] A degeneracy condition for a bounded branching process. Mat. Zametki 8 (1970) 9-18. | MR | Zbl
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