An ergodic theorem for the extremal process of branching Brownian motion

被引：3

作者：

Arguin, Louis-Pierre ^{[1
]}

Bovier, Anton ^{[2
]}

Kistler, Nicola ^{[3
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3T 1JA, Canada

[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[3] CUNY Coll Staten Isl, Dept Math, Staten Isl, NY 10314 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2015年 / 51卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Branching Brownian motion; Ergodicity; Extreme value theory; KPP equation and traveling waves; STATISTICS;

D O I：

10.1214/14-AIHP608

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：

In a previous paper, the authors proved a conjecture of Lalley and Sellke that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a Gumbel distribution. The result is extended here to the entire system of particles that are extremal, i.e. close to the maximum. Namely, it is proved that the distribution of extremal particles under time-average converges to a Poisson cluster process.

引用

页码：557 / 569

页数：13

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