On the rates of convergence for sums of dependent random variables

Abstract

For a sequence $\{X_n,n⩾1\}$ of nonnegative random variables where $\max [\min (X_n-s,t),0]$, $t>s⩾0$, satisfy a moment inequality, sufficient conditions are given under which ${\sum }_{k=1}^n(X_k-\mathbb{E}{X}_k)/b_n\stackrel{a.s.}{⟶}0$. Our statement allows us to obtain a strong law of large numbers for sequences of pairwise negatively quadrant dependent random variables under sharp normalising constants.

17 pages

Cited by in corpus (1)

• On the complete convergence for sequences of dependent random variables via stochastic domination conditions and regularly varying functions theory