Cesàro Summation for Random Fields

Allan Gut () and Ulrich Stadtmüller ()
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Allan Gut: Uppsala University
Ulrich Stadtmüller: Ulm University

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 715-728

Abstract: 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.

Keywords: Cesàro summation; Sums of i.i.d. random variables; Complete convergence; Convergence in probability; Almost sure convergence; Strong law of large numbers; 60F15; 60G50; 60G60; 40G05; 60F05 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0223-9

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