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arXiv · 2011.10262

On the rates of convergence for sums of dependent random variables

João Lita da Silva
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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.

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João Lita da Silva. 2020-11-20. On the rates of convergence for sums of dependent random variables. https://arxiv.org/abs/2011.10262

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