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The size of the averages of strongly mixing random variables

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  • Rieders, Eric

Abstract

Mixing conditions have frequently been found to be satisfactory substitutes for independence in attempts to generalize the classical limit theorems of probability theory. We find that there is a natural way to classify stationary sequences with respect to the way in which the sizes of the corresponding averages are controlled by the moments of the marginal distribution, using two of the standard mixing conditions. Stationary sequences of [phi]-mixing random variables have averages controlled by their moments in the same way as independent sequences, whereas the weaker condition of strong mixing is shown, via examples, not to in general imply results analogous to the classical theorems.

Suggested Citation

  • Rieders, Eric, 1993. "The size of the averages of strongly mixing random variables," Statistics & Probability Letters, Elsevier, vol. 18(1), pages 57-64, August.
    • Handle: RePEc:eee:stapro:v:18:y:1993:i:1:p:57-64
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    Cited by:

    1. Santanu Dutta & Tushar Kanti Powdel, 2023. "Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 257-289, May.
    2. Banys, Povilas & Davydov, Youri & Paulauskas, Vygantas, 2010. "Remarks on the SLLN for linear random fields," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 489-496, March.

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