On the rates of convergence for sums of dependent random variables

João Lita da Silva

On the rates of convergence for sums of dependent random variables

Probability 2020-11-23 v1

Authors: João Lita da Silva

Abstract

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of nonnegative random variables where $\max[\min(X_{n} - s,t),0]$ , $t > s \geqslant 0$ , satisfy a moment inequality, sufficient conditions are given under which $\sum_{k=1}^n (X_k - \mathbb{E} \, X_k)/b_n \overset{\mathrm{a.s.}}{\longrightarrow} 0$ . 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.

Keywords

dependent random variables rates of convergence moment inequality strong law of large numbers negatively quadrant dependent

Cite

@article{arxiv.2011.10262,
  title  = {On the rates of convergence for sums of dependent random variables},
  author = {João Lita da Silva},
  journal= {arXiv preprint arXiv:2011.10262},
  year   = {2020}
}

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17 pages

On the rates of convergence for sums of dependent random variables

Abstract

Keywords

Cite

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