On complete convergence for randomly indexed sums for a case without identical distributions.

Kuczmaszewska, Anna; Szynal, Dominik

Displaying similar documents to “On complete convergence for randomly indexed sums for a case without identical distributions.”

Random sum Limit Theorems for Nonidentically Distributed Random Variables

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Complete convergence of weighted sums for arrays of rowwise $ϕ$ -mixing random variables

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In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise $ϕ$ -mixing random variables, and the Baum-Katz-type result for arrays of rowwise $ϕ$ -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of $ϕ$ -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).

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On the convergence of moments in the CLT for triangular arrays with an application to random polynomials

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We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.

Strong Convergence for weighed sums of negatively superadditive dependent random variables

Zhiyong Chen, Haibin Wang, Xuejun Wang, Shuhe Hu (2016)

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In this paper, the strong law of large numbers for weighted sums of negatively superadditive dependent (NSD, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng ([2]) for independent and identically distributed random variables to the case of NSD random variables.