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The strong law of large numbers for weighted averages under dependence assumptions

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Abstract

Strong laws of large numbers (SLLN) for weighted averages are proved under various dependence assumptions when the variables are not necessarily independent or identically distributed. The results considerably extend the existing results. Weighted versions of the Marcinkiewicz-Zygmund SLLN are also formulated and proved under a similar set up. It seems that such results are not known even for independent and identically distributed random variables.

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Authors and Affiliations

  1. Division of Theoretical Statistics and Mathematics, Indian Statistical Institute, 203 B. T. Road, 700035, Calcutta, India

    Tapas K. Chandra & Subhashis Ghosal

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  1. Tapas K. Chandra
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  2. Subhashis Ghosal
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Chandra, T.K., Ghosal, S. The strong law of large numbers for weighted averages under dependence assumptions. J Theor Probab 9, 797–809 (1996). https://doi.org/10.1007/BF02214087

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  • DOI: https://doi.org/10.1007/BF02214087

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