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On the LSL for Random Fields

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Abstract

In some earlier work, we have considered extensions of Lai’s (Ann. Probab. 2:432–440, 1974) law of the single logarithm for delayed sums to a multi-index setting with the same as well as different expansion rates in the various dimensions. A further generalization concerns window sizes that are regularly varying with index 1 (on the line). In the present paper, we establish multi-index versions of the latter as well as for some mixtures of expansion rates. In order to keep things within reasonable size, we confine ourselves to some special cases for the index set \(\mathbb{Z}_{+}^{2}\) .

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Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden

    Allan Gut

  2. Department of Number Theory and Probability Theory, Ulm University, 89069, Ulm, Germany

    Ulrich Stadtmüller

Authors
  1. Allan Gut
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  2. Ulrich Stadtmüller
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Correspondence to Allan Gut.

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Gut, A., Stadtmüller, U. On the LSL for Random Fields. J Theor Probab 24, 422–449 (2011). https://doi.org/10.1007/s10959-009-0265-z

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  • DOI: https://doi.org/10.1007/s10959-009-0265-z

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