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.
Publié le : 1998-01-14
Classification:
Winding angle,
Brownian motion,
random walk,
strong approximation,
60J65,
60J15,
60F15
@article{1022855413,
author = {Shi, Zhan},
title = {Windings of Brownian motion and random walks in the
plane},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 112-131},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855413}
}
Shi, Zhan. Windings of Brownian motion and random walks in the
plane. Ann. Probab., Tome 26 (1998) no. 1, pp. 112-131. http://gdmltest.u-ga.fr/item/1022855413/