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On the LSL for Random Fields

Author

Listed:
  • Allan Gut

    (Uppsala University)

  • Ulrich Stadtmüller

    (Ulm University)

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 $\mathbb{Z}_{+}^{2}$ .

Suggested Citation

  • Allan Gut & Ulrich Stadtmüller, 2011. "On the LSL for Random Fields," Journal of Theoretical Probability, Springer, vol. 24(2), pages 422-449, June.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:2:d:10.1007_s10959-009-0265-z
    DOI: 10.1007/s10959-009-0265-z
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    References listed on IDEAS

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    1. Paranjape, S. R. & Park, C., 1973. "Laws of iterated logarithm of multiparameter wiener processes," Journal of Multivariate Analysis, Elsevier, vol. 3(1), pages 132-136, March.
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