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Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications

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Book cover High Dimensional Probability III

Part of the book series: Progress in Probability ((PRPR,volume 55))

Abstract

We consider strong limit theorems such as bounded and compact laws of the iterated logarithm and an almost sure invariance principle for mixing random variables with values in Hilbert space. Applying these results we prove an almost sure invariance principle for U-statistics as well.

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Author information

Authors and Affiliations

  1. Department of Probability Theory, Institute of Mathematics, Uzbek Academy of Sciences, 29, F. Khodjaev str., 700143, Tashkent, Uzbekistan

    Olimjon Sh. Sharipov

Authors
  1. Olimjon Sh. Sharipov
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Aarhus, Building 530 Ny Munkegade, Arhus C, 8000, Denmark

    Jørgen Hoffmann-Jørgensen

  2. Department of Statistics, University of Washington, Box 354322, Seattle, WA, 98195-4322, USA

    Jon A. Wellner

  3. Department of Mathematics, City College, New York, NY, 10031, USA

    Michael B. Marcus

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© 2003 Springer Basel AG

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Sharipov, O.S. (2003). Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications. In: Hoffmann-Jørgensen, J., Wellner, J.A., Marcus, M.B. (eds) High Dimensional Probability III. Progress in Probability, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8059-6_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8059-6_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9423-4

  • Online ISBN: 978-3-0348-8059-6

  • eBook Packages: Springer Book Archive

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