An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables

Author:

Huang Haiwu1,Yuan Yuan1,Zeng Hongguo2

Affiliation:

1. School of Science, Guilin University of Aerospace Technology, Guilin 541004, China

2. Library, Guilin University of Aerospace Technology, Guilin 541004, China

Abstract

<abstract><p>The authors study the convergence rate of complete moment convergence for weighted sums of weakly dependent random variables without assumptions of identical distribution. Under the moment condition of $ E{{{\left| X \right|}^{\alpha }}}/{{{\left(\log \left(1+\left| X \right| \right) \right)}^{\alpha /\gamma -1}}}\; &lt; \infty $ for $ 0 &lt; \gamma &lt; \alpha $ with $ 1 &lt; \alpha \le 2 $, we establish the complete $ \alpha $-th moment convergence theorem for weighted sums of weakly dependent cases, which improves and extends the related known results in the literature.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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