Abstract
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.
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R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30.
R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29.
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Adamczak, R., Latała, R. The LIL for U-Statistics in Hilbert Spaces. J Theor Probab 21, 704–744 (2008). https://doi.org/10.1007/s10959-007-0134-6
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DOI: https://doi.org/10.1007/s10959-007-0134-6