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The strong laws of large numbers for positive measurable operators and applications

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  • Quang, Nguyen Van
  • Son, Do The
  • Son, Le Hong

Abstract

The aim of this study is to establish some strong laws of large numbers for positive measurable operators under various conditions. As applications, several results on strong laws of large numbers for pairwise independent non-identically distributed random variables and for pairwise independent identically distributed random variables have been generalized to the noncommutative context. The results obtained are more general than some related results previously reported.

Suggested Citation

  • Quang, Nguyen Van & Son, Do The & Son, Le Hong, 2017. "The strong laws of large numbers for positive measurable operators and applications," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 110-120.
    • Handle: RePEc:eee:stapro:v:124:y:2017:i:c:p:110-120
    DOI: 10.1016/j.spl.2017.01.014
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    References listed on IDEAS

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    1. Chen, Pingyan & Sung, Soo Hak, 2016. "A strong law of large numbers for nonnegative random variables and applications," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 80-86.
    2. Korchevsky, Valery, 2015. "A generalization of the Petrov strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 102-108.
    3. Quang, Nguyen Van & Huy, Nguyen Ngoc & Son, Le Hong, 2013. "The degenerate convergence criterion and Feller’s weak law of large numbers for double arrays in noncommutative probability," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1812-1818.
    4. Etemadi, Nasrollah, 1983. "On the laws of large numbers for nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 187-193, March.
    5. Chen, Pingyan & Sung, Soo Hak, 2016. "On the strong laws of large numbers for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 87-93.
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