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On the law of large numbers for stationary sequences

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  • Maller, R. A.

Abstract

We show that if Xi is a stationary sequence for which Sn/Bn converges to a finite non zero random variable of constant sign, where Sn=X1+X2+...+Xn and Bn is a sequence of constants, then Bn is regularly varying with index 1. If in addition [Sigma]P(X1>Bn is finite, then EX1 is finite, and if in addition to this Xi satisfies an asymptotic independence condition, EX1 [not equal to] 0.

Suggested Citation

  • Maller, R. A., 1980. "On the law of large numbers for stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 10(1), pages 65-73, June.
    • Handle: RePEc:eee:spapps:v:10:y:1980:i:1:p:65-73
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    Cited by:

    1. Fakhreddine Boukhari, 2022. "On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2068-2079, September.
    2. Rosalsky, Andrew & Stoica, George, 2010. "On the strong law of large numbers for identically distributed random variables irrespective of their joint distributions," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1265-1270, September.

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