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Mean Convergence Theorems for Weighted Sums of Arrays of Residually h-integrable Random Variables Concerning the Weights under Dependence Assumptions

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Abstract

From the classical notion of uniform integrability of a sequence of random variables, a new concept called residual h-integrability is introduced for an array of random variables, concerning an array of constants, which is weaker than other previous related notions of integrability.

Martingale difference, pairwise negative quadrant dependence, tail φ-mixing property and L p -mixingale are four special kinds of dependence structures, where 1≤p≤2. By relating the residual h-integrability with such these dependence assumptions, some conditions are formulated under which mean convergence theorems for weighted sums of arrays of random variables are established, and many earlier results are explained as the special cases of the ones appearing in our present work.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China

    Demei Yuan & Bao Tao

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  1. Demei Yuan
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  2. Bao Tao
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Correspondence to Demei Yuan.

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Yuan, D., Tao, B. Mean Convergence Theorems for Weighted Sums of Arrays of Residually h-integrable Random Variables Concerning the Weights under Dependence Assumptions. Acta Appl Math 103, 221–234 (2008). https://doi.org/10.1007/s10440-008-9232-4

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  • DOI: https://doi.org/10.1007/s10440-008-9232-4

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