Journal of Theoretical Probability

, Volume 21, Issue 3, pp 704–744 | Cite as

The LIL for U-Statistics in Hilbert Spaces

  • Radosław AdamczakEmail author
  • Rafał Latała


We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest.


U-statistics Tail and moment estimates Law of the iterated logarithm 

Mathematics Subject Classification (2000)

60F15 60E15 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute of MathematicsPolish Academy of SciencesWarszawaPoland
  2. 2.Institute of MathematicsWarsaw UniversityWarszawaPoland

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