An almost sure invariance principle for the range of planar random walks

被引：10

作者：

Bass, RF ^{[1
]}

Rosen, J

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] CUNY Coll Staten Isl, Staten Isl, NY 10314 USA

来源：

ANNALS OF PROBABILITY | 2005年 / 33卷 / 05期

关键词：

range; random walks; invariance principle; intersection local time; Wiener sausage; Brownian motion;

D O I：

10.1214/009117905000000215

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：

For a symmetric random walk in Z(2) with 2 + delta moments, we represent vertical bar R(n)vertical bar, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each k >= 1 [Graphics] where Wt is a Brownian motion, W(t)((n)) = Wnt/root n, gamma j,n is the renormalized intersection local time at time 1 for W((n)) and c(X) is a constant depending on the distribution of the random walk.

引用

页码：1856 / 1885

页数：30

共 24 条

[1]

[Anonymous], LOCAL QUANTUM THEORY

[2]

BASS RF, 1993, ANN I H POINCARE-PR, V29, P419

[3] Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm [J].