Abstract
We establish a bounded and a compact law of the iterated logarithm for partial sum processes indexed by classes of functions. We assume a growth condition on the metric entropy under bracketing. Examples show that our results are sharp. As a corollary we obtain new results for weighted sums of independent identically distributed random variables.
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Lacey, M. Laws of the iterated logarithm for partial sum processes indexed by functions. J Theor Probab 2, 377–398 (1989). https://doi.org/10.1007/BF01054022
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DOI: https://doi.org/10.1007/BF01054022