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Convergence in the pth-mean and some Weak Laws of Large Numbers for weighted sums of random elements in separable normed linear spaces

Author

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  • Wang, Xiang Chen
  • Bhaskara Rao, M.

Abstract

. Let Xn, n >= 1, be a sequence of tight random elements taking values in a separable Banach space B such that Xn, n >= 1, is uniformly integrable. Let ank, n >= 1, k >= 1, be a double array of real numbers satisfying [Sigma]k >= 1 ank = 1 for some positive constant [Gamma]. Then [Sigma]k >= 1 ankXk, n >= 1, converges to 0 in probability if and only if [Sigma]k >= 1 ankf(Xk), n >= 1, converges to 0 in probability for every f in the dual space B*.

Suggested Citation

  • Wang, Xiang Chen & Bhaskara Rao, M., 1984. "Convergence in the pth-mean and some Weak Laws of Large Numbers for weighted sums of random elements in separable normed linear spaces," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 124-134, August.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:1:p:124-134
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