Cesàro α-Integrability and Laws of Large Numbers-II

T. K. Chandra () and A. Goswami ()
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T. K. Chandra: Indian Statistical Institute
A. Goswami: Indian Statistical Institute

Journal of Theoretical Probability, 2006, vol. 19, issue 4, 789-816

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

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; Primary 60F15; Secondary 60F05 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0038-x

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