The spread of a catalytic branching random walk

被引：24

作者：

Carmona, Philippe ^{[1
]}

Hu, Yueyun ^{[2
]}

机构：

[1] Univ Nantes, Lab Jean Leray, UMR 6629, F-44322 Nantes 03, France

[2] Univ Paris 13, Dept Math, Inst Galilee, LAGA UMR 7539, F-93430 Villetaneuse, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2014年 / 50卷 / 02期

关键词：

Branching processes; Catalytic branching random walk; MARTINGALE CONVERGENCE; MINIMAL POSITION; BROWNIAN-MOTION; THEOREM;

D O I：

10.1214/12-AIHP529

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 catalytic branching random walk on Z that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position M,,: For some constant alpha , M-n/n -> alpha almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for M-n - alpha n as n goes to infinity.

引用

页码：327 / 351

页数：25

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