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.

引用

页码：959 / 993

页数：35

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