Summary
For a set of i.i.d. random variables indexed by the positive integer d-dimensional lattice points we give conditions for the existence of moments of the supremum of normed partial sums, thereby obtaining results related to the Kolmogorov-Marcinkiewicz strong law of large numbers and the law of the iterated logarithm.
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Gut, A. Moments of the maximum of normed partial sums of random variables with multidimensional indices. Z. Wahrscheinlichkeitstheorie verw Gebiete 46, 205–220 (1979). https://doi.org/10.1007/BF00533260
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DOI: https://doi.org/10.1007/BF00533260