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Cesàro Summation for Random Fields

Author

Listed:
  • Allan Gut

    (Uppsala University)

  • Ulrich Stadtmüller

    (Ulm University)

Abstract

Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of i.i.d. random variables. The natural extension of results corresponding to Cesàro summation amounts to proving almost sure convergence of the Cesàro means. In the present paper we extend such results as well as weak laws and results on complete convergence to random fields, more specifically to random variables indexed by ℤ + 2 , the positive two-dimensional integer lattice points.

Suggested Citation

  • Allan Gut & Ulrich Stadtmüller, 2010. "Cesàro Summation for Random Fields," Journal of Theoretical Probability, Springer, vol. 23(3), pages 715-728, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-009-0223-9
    DOI: 10.1007/s10959-009-0223-9
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    References listed on IDEAS

    as
    1. Gut, Allan & Stadtmüller, Ulrich, 2009. "An asymmetric Marcinkiewicz-Zygmund LLN for random fields," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1016-1020, April.
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