Displaying similar documents to “Exact rate of convergence for increments of random fields.”

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

Christophe Cuny, Michel Weber (2006)

Colloquium Mathematicae

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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.

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

Xinghui Wang, Xiaoqin Li, Shuhe Hu (2014)

Applications of Mathematics

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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).