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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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Brownian motion, Strassen's law of iterated logarithm
Language:English
Date:1978
Deposited On:30 Oct 2009 16:38
Last Modified:24 Sep 2019 16:20
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/aop/1176995487
Related URLs:http://www.zentralblatt-math.org/zmath/en/search/?q=an:0391.60036

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