Here there is derived a condition on sequences $\varepsilon_n \downarrow 0$ which implies that $P\lbrack W(n^\bullet)/(2n \log \log n)^\frac{1}{2} \not\in K^\varepsilon n \mathrm{i.o.}\rbrack = 0$, where $W$ is the Wiener process and $K$ is the compact set in Strassen's law of the iterated logarithm. A similar result for random walks is also given.
Publié le : 1978-08-14
Classification:
Brownian motion,
Strassen's law of iterated logarithm,
60F15,
60J15
@article{1176995487,
author = {Bolthausen, E.},
title = {On the Speed of Convergence in Strassen's Law of the Iterated Logarithm},
journal = {Ann. Probab.},
volume = {6},
number = {6},
year = {1978},
pages = { 668-672},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995487}
}
Bolthausen, E. On the Speed of Convergence in Strassen's Law of the Iterated Logarithm. Ann. Probab., Tome 6 (1978) no. 6, pp. 668-672. http://gdmltest.u-ga.fr/item/1176995487/