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A conditional version of the extended Kolmogorov–Feller weak law of large numbers

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  • Yuan, Demei
  • Hu, Xuemei

Abstract

A conditional version of the extended Kolmogorov–Feller weak law of large numbers is established, which generalizes the existing results and is actually adapted to a sequence of exchangeable random variables provided the conditional σ-algebra is taken as the tail σ-algebra or the σ-algebra of permutable events of such a sequence.

Suggested Citation

  • Yuan, Demei & Hu, Xuemei, 2015. "A conditional version of the extended Kolmogorov–Feller weak law of large numbers," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 99-107.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:99-107
    DOI: 10.1016/j.spl.2014.11.006
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    References listed on IDEAS

    as
    1. Wang, Xinghui & Wang, Xuejun, 2013. "Some inequalities for conditional demimartingales and conditional N-demimartingales," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 700-709.
    2. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    3. Manuel Ordóñez Cabrera & Andrew Rosalsky & Andrei Volodin, 2012. "Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 369-385, June.
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    Cited by:

    1. Antonio Avilés López & José Miguel Zapata García, 2020. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations," Mathematics, MDPI, vol. 8(10), pages 1-23, October.

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