Strong laws of large numbers for pairwise quadrant dependent random variables

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Abstract

For a sequence {Xn,n⩾1} of quadrant dependent random variables satisfying EXn<∞ for all n⩾1 and a family of positive sequences {bn}, we give sufficient conditions to obtain ∑k=1 n(Xk−EXk)∕bn⟶a.s.0. For random sequences which are additionally stochastically dominated by a random variable X∈ℒp, 1<p<2, we shall prove strong laws of large numbers under normalising sequences asymptotically equivalent to n1∕p, 1<p<2 up to a logarithm power.

Original languageEnglish
Pages (from-to)349-358
Number of pages10
JournalStatistics and Probability Letters
Volume137
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • Quadrant dependent random variables
  • Strong law of large numbers

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