Cesàro α-Integrability and Laws of Large Numbers-II |
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Authors: | T K Chandra A Goswami |
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Institution: | (1) Division of Theoretical Statistics and Mathematics, Indian Statistical Institute, 203 B. T. Road, Calcutta, 700 108, India |
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Abstract: | For a sequence of random variables, a new set of properties called Cesàro α-Integrability and Strong Cesàro α-Integrability
was recently introduced in an earlier paper and these properties were used to prove several new laws of large numbers, namely
both Strong and Weak Laws of Large Numbers for pairwise-independent random variables as well as WLLN for some dependent sequences
of random variables. In this paper, a set of weaker conditions called Residual Cesàro α-Integrability and Strong Residual
Cesàro α-Integrability are introduced and significant improvements over earlier results are obtained. In addition, new results
on L
p
-convergence, for 0 < p < 2, and SLLN for some dependent sequences are proved.
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Keywords: | Weak law of large numbers Strong law of large numbers uniform integrability Cesàro uniform integrability pairwise uncorrelated pairwise-independent martingale difference sequence Φ -mixing sequence α -mixing sequence AQI AQSI |
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