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.

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.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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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: | 05 Apr 2016 13:30 |

Publisher: | Institute of Mathematical Statistics |

ISSN: | 0091-1798 |

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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