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Strong laws of large numbers for arrays of rowwise conditionally independent random elements

Author

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  • Ronald Frank Patterson
  • Abolghassem Bozorgnia
  • Robert Lee Taylor

Abstract

Let { X n k } be an array of rowwise conditionally independent random elements in a separable Banach space of type p , 1 ≤ p ≤ 2 . Complete convergence of n − 1 r ∑ k = 1 n X n k to 0 , 0 < r < p ≤ 2 is obtained by using various conditions on the moments and conditional means. A Chung type strong law of large numbers is also obtained under suitable moment conditions on the conditional means.

Suggested Citation

  • Ronald Frank Patterson & Abolghassem Bozorgnia & Robert Lee Taylor, 1993. "Strong laws of large numbers for arrays of rowwise conditionally independent random elements," International Journal of Stochastic Analysis, Hindawi, vol. 6, pages 1-9, January.
    • Handle: RePEc:hin:jnijsa:637938
    DOI: 10.1155/S1048953393000012
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