Windings of Brownian motion and random walks in the plane

被引：0

作者：

Shi, Z ^{[1
]}

机构：

[1] Univ Paris 06, LSTA, URA 1321, F-75252 Paris 05, France

来源：

ANNALS OF PROBABILITY | 1998年 / 26卷 / 01期

关键词：

winding angle; Brownian motion; random walk; strong approximation;

D O I：

暂无

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 are interested in the almost sure asymptotic behavior of the windings of planar Brownian motion. Both the usual lim sup and Chung's lim inf versions of the law of the iterated logarithm are presented for the so-called "big" and "small" winding angles. Our method is based on some very accurate estimates of the winding clock. The corresponding problem for a spherically symmetric random walk in R-2 is also studied. A strong approximation using the Brownian big winding process is established. Similar results are obtained.

引用

页码：112 / 131

页数：20

共 36 条

[1]

[Anonymous], 1994, LECT NOTES MATH

[2] WINDINGS OF SPHERICALLY SYMMETRICAL RANDOM-WALKS VIA BROWNIAN EMBEDDING [J].