MARTIN BOUNDARY OF A KILLED RANDOM WALK ON A QUADRANT

被引：24

作者：

Ignatiouk-Robert, Irina ^{[1
]}

Loree, Christophe ^{[1
]}

机构：

[1] Univ Cergy Pontoise, CNRS, UMR 8088, F-95302 Cergy Pontoise, France

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 03期

关键词：

Martin boundary; sample path large deviations; random walk;

D O I：

10.1214/09-AOP506

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：

A complete representation of the Martin boundary of killed random walks on the quadrant N* x N* is obtained. It is proved that the corresponding full Martin compactification of the quadrant N* x N* is homeomorphic to the closure of the set {w = z/(1 +vertical bar z vertical bar) : Z is an element of N* x N*} in R(2). The method is based on a ratio limit theorem for local processes and large deviation techniques.

引用

页码：1106 / 1142

页数：37

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