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2016•数学季刊：英文版Requires access

Complete Convergence for Weighted Sums of WOD Random Variables

Zhang Zhang, Ying, Yu, Shen, Ai-ting

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Abstract

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

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What this paper is about

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

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Available abstract

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

Key concepts: Orthant, Mathematics, Convergence of random variables, Random variable, Proofs of convergence of random variables, Sum of normally distributed random variables, Convergence (economics), Algebra of random variables

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