## The Annals of Probability

### Windings of Brownian motion and random walks in the plane

Zhan Shi

#### Abstract

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 $\mathbb{R}^2$ is also studied. A strong approximation using the Brownian big winding process is established. Similar results are obtained.

#### Article information

Source
Ann. Probab., Volume 26, Number 1 (1998), 112-131.

Dates
First available in Project Euclid: 31 May 2002

https://projecteuclid.org/euclid.aop/1022855413

Digital Object Identifier
doi:10.1214/aop/1022855413

Mathematical Reviews number (MathSciNet)
MR1617043

Zentralblatt MATH identifier
0938.60073

Subjects
Secondary: 60F15: Strong theorems

#### Citation

Shi, Zhan. Windings of Brownian motion and random walks in the plane. Ann. Probab. 26 (1998), no. 1, 112--131. doi:10.1214/aop/1022855413. https://projecteuclid.org/euclid.aop/1022855413

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