THE SENETA-HEYDE SCALING FOR THE BRANCHING RANDOM WALK

被引：53
|
作者：
Aidekon, Elie [1 ]
Shi, Zhan [1 ]
机构：
[1] Univ Paris 06, Probabil Lab, UMR 7599, F-75252 Paris 05, France
来源：
ANNALS OF PROBABILITY | 2014年 / 42卷 / 03期
关键词：
Branching random walk; Seneta-Heyde norming; additive martingale; derivative martingale; GALTON-WATSON PROCESS; BROWNIAN-MOTION; MARTINGALE CONVERGENCE; MINIMAL POSITION; TRAVELING-WAVES; FIXED-POINTS; EQUATION; TREES; ABSORPTION; SURVIVAL;
D O I：
10.1214/12-AOP809
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631] in a one-dimensional supercritical branching random walk, and study the additive martingale (W-n). We prove that, upon the system's survival, n(1/2)W(n) converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou, of the derivative martingale.
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页码：959 / 993
页数：35
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