Mean convergence theorems for weighted sums of arrays of residually \(h\)-integrable random variables concerning the weights under dependence assumptions

DOI10.1007/s10440-008-9232-4zbMath1153.60333OpenAlexW1996836289MaRDI QIDQ959986

Bao Tao, De-Mei Yuan

Publication date: 16 December 2008

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-008-9232-4

zbMATH Keywords

negative quadrant dependencemartingale difference array\(L_p\)-mixingale arrayresidual \(h\)-integrabilityresidual Cesàro \(\alpha \)-integrabilitytail \(\varphi\)-mixing array

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (11)

Limiting behaviour for arrays of rowwise widely orthant dependent random variables under conditions of R − h-integrability and its applications ⋮ Conditional limit theorems for conditionally negatively associated random variables ⋮ Moment Inequalities for $m$-NOD Random Variables and Their Applications ⋮ Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications ⋮ Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables ⋮ Unnamed Item ⋮ Convergence in \(p\)-mean for arrays of row-wise extended negatively dependent random variables ⋮ Convergence in \(p\)-mean for arrays of random variables ⋮ Mean convergence theorems for weighted sums of random variables under a condition of weighted integrability ⋮ Weak laws of large numbers for arrays of dependent random variables ⋮ Conditional mean convergence theorems of conditionally dependent random variables under conditions of integrability

Cites Work

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• Cesàro \(\alpha\)-integrability and laws of large numbers. II
• A maximal inequality and dependent strong laws
• Convergence of weighted sums of random variables and uniform integrability concerning the weights
• Cesàro \({\alpha}\)-integrability and laws of large numbers. I
• Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability
• Negative association of random variables, with applications
• On the convergence of weighted sums of \(L_q\)-mixingale arrays
• Some Concepts of Dependence
• On the $L_p$-Convergence for $n^{-1/p} S_n, 0 < p < 2^1$

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