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Moving averages. (English) Zbl 0684.60023

Almost everywhere convergence, Proc. Int. Conf., Columbus/OH 1988, 131-144 (1989).
[For the entire collection see Zbl 0679.00012.]
Main aim of the present paper is to discuss possible refinements of the strong law of large numbers for means of i.i.d. random variables \(X;X_ 1,X_ 2,...\). Several characterizations are obtained in terms of Césaro-, Riesz-, and “moving average”-summability. More general moment conditions than E \(| X|^ p<\infty\) can be handled by using general self-neglecting functions \(\phi\) instead of \(\phi (x)=x^{1/p}\). Finally, it is briefly outlined how the results relate to certain almost sure invariance or non-invariance principles for partial sums. For sake of comparison several references are provided concerning the ergodic, dependent or Banach-valued cases.
Reviewer: J.Steinebach

MSC:

60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
40G05 Cesàro, Euler, Nörlund and Hausdorff methods

Citations:

Zbl 0679.00012