CRITICAL BROWNIAN SHEET DOES NOT HAVE DOUBLE POINTS

被引：12

作者：

Dalang, Robert C. ^{[1
]}

Khoshnevisan, Davar ^{[2
]}

Nualart, Eulalia ^{[3
]}

Wu, Dongsheng ^{[4
]}

Xiao, Yimin ^{[5
]}

机构：

[1] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[3] Univ Paris 13, Inst Galilee, F-93430 Villetaneuse, France

[4] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

[5] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

ANNALS OF PROBABILITY | 2012年 / 40卷 / 04期

基金：

瑞士国家科学基金会; 美国国家科学基金会;

关键词：

Brownian sheet; multiple points; capacity; Hausdorff dimension; DIMENSION; GEOMETRY; IMAGES;

D O I：

10.1214/11-AOP665

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 derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d - 2N) = d.

引用

页码：1829 / 1859

页数：31

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