Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF COORDINATEWISE NEGATIVELY ASSOCIATED RANDOM VECTORS IN HILBERT SPACES

  • Received : 2021.07.11
  • Accepted : 2021.11.08
  • Published : 2022.07.31
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Abstract

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, Xn, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.

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References

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