Windings of Brownian motion and random walks in the plane

• 成果类型: Article
• 署名作者: Shi, Z
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 112-131
• 关键词: asymptotic laws

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.