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Probability in Banach Spaces pp 196–234Cite as

The Law of the Iterated Logarithm

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete ((CLASSICS,volume 23))

Abstract

This chapter is devoted to the classical laws of the iterated logarithm of Kolmogorov and Hartman-Wintner-Strassen in the vector valued setting. These extensions both enlighten the scalar statements and describe various new interesting phenomena in the infinite dimensional setting. As in the previous chapter on the strong law of large numbers, the isoperimetric approach proves to be an efficient tool in this study. The main results described here show again how the strong almost sure statement of the law of the iterated logarithm reduces to the corresponding (necessary) statement in probability, under moment conditions similar to those of the scalar case.

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Notes and References

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Author information

Authors and Affiliations

  1. Institut de Recherche Mathématique Avancée, Département de Mathématique, Université Louis Pasteur, F-67084, Strasbourg, France

    Michel Ledoux

  2. Equipe d’Analyse, Université de Paris VI, F-75252, Paris, France

    Michel Talagrand

  3. Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA

    Michel Talagrand

Authors
  1. Michel Ledoux
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  2. Michel Talagrand
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© 1991 Springer-Verlag Berlin Heidelberg

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Ledoux, M., Talagrand, M. (1991). The Law of the Iterated Logarithm. In: Probability in Banach Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20212-4_10

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  • DOI: https://doi.org/10.1007/978-3-642-20212-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20211-7

  • Online ISBN: 978-3-642-20212-4

  • eBook Packages: Springer Book Archive

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