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

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Abstract

For a triangular array \({\{a_{n, k}, 1 \leqq k \leqq n, n \geqq 1\}}\) of real numbers and a sequence of random variables \({\{X_{n}, n \geqq 1\}}\) conditions are given to ensure \({\sum_{k=1}^{n} a_{n,k} (X_{k} - \mathbb{E} X_{k}) \overset{\textnormal{a.s.}}{\longrightarrow} 0}\) Namely, the sequence \({\{X_{n}, n\geqq1\}}\) will be considered extended negatively dependent and either (i) stochastically dominated by a random variable X satisfying \({\mathbb{E}|X|^{p} < \infty}\) for some \({1 < p < 2}\) or (ii) identically distributed such that \({\mathbb{E}|X_{1}| < \infty}\).

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  1. Department of Mathematics and CMA, Faculty of Sciences and Technology, New University of Lisbon, Quinta da Torre, 2829-516, Caparica, Portugal

    J. Lita da Silva

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  1. J. Lita da Silva
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Silva, J.L.d. Almost sure convergence for weighted sums of extended negatively dependent random variables. Acta Math. Hungar. 146, 56–70 (2015). https://doi.org/10.1007/s10474-015-0502-0

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