Almost sure convergence for weighted sums of extended negatively dependent random variables

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Abstract

For a triangular array $${\{a_{n, k}, 1 \leqq k \leqq n, n \geqq 1\}}$${an,k,1≦k≦n,n≧1} of real numbers and a sequence of random variables $${\{X_{n}, n \geqq 1\}}$${Xn,n≧1} conditions are given to ensure $${\sum_{k=1}^{n} a_{n,k} (X_{k} - \mathbb{E} X_{k}) \overset{\textnormal{a.s.}}{\longrightarrow} 0}$$∑k=1nan,k(Xk-EXk)⟶a.s.0 Namely, the sequence $${\{X_{n}, n\geqq1\}}$${Xn,n≧1} will be considered extended negatively dependent and either (i) stochastically dominated by a random variable X satisfying $${\mathbb{E}|X|^{p}E|X|p

Original languageEnglish
Article number502
Pages (from-to)56-70
Number of pages15
JournalActa Mathematica Hungarica
Volume146
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • weighted sum
  • extended negatively dependent random variable
  • strong law of large numbers

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