A NECESSARY AND SUFFICIENT CONDITION FOR THE NONTRIVIAL LIMIT OF THE DERIVATIVE MARTINGALE IN A BRANCHING RANDOM WALK

被引：22

作者：

Chen, Xinxin ^{[1
]}

机构：

[1] Univ Paris 06, F-75005 Paris, France

来源：

ADVANCES IN APPLIED PROBABILITY | 2015年 / 47卷 / 03期

关键词：

Branching random walk; derivative martingale; Mandelbrot's cascade; random walk conditioned to stay positive; BROWNIAN-MOTION; FIXED-POINTS; CONVERGENCE; THEOREM; TREES;

D O I：

10.1017/S0001867800048813

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 a branching random walk. Biggins and Kyprianou (2004) proved that, in the boundary case, the associated derivative martingale converges almost surely to a finite nonnegative limit, whose law serves as a fixed point of a smoothing transformation (Mandelbrot's cascade). In this paper, we give a necessary and sufficient condition for the nontriviality of the limit in this boundary case.

引用

页码：741 / 760

页数：20

共 18 条

[1] CONVERGENCE IN LAW OF THE MINIMUM OF A BRANCHING RANDOM WALK [J].