# On the speed of convergence in Strassen's law of the iterated logarithm

Bolthausen, E (1978). On the speed of convergence in Strassen's law of the iterated logarithm. The Annals of Probability, 6(4):668-672.

## Abstract

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.

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.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Brownian motion; Strassen's law of iterated logarithm English 1978 30 Oct 2009 16:38 05 Apr 2016 13:30 Institute of Mathematical Statistics 0091-1798 https://doi.org/10.1214/aop/1176995487 http://www.zentralblatt-math.org/zmath/en/search/?q=an:0391.60036
Permanent URL: https://doi.org/10.5167/uzh-23149