| 郭明乐,祝东进.$\rho^*$-混合随机变量列加权和的完全收敛性[J].数学研究及应用,2013,33(4):483~492 |
| $\rho^*$-混合随机变量列加权和的完全收敛性 |
| Complete Convergence of Weighted Sums for $\rho^*$-Mixing Sequence of Random Variables |
| 投稿时间：2012-05-06 修订日期：2012-09-03 |
| DOI：10.3770/j.issn:2095-2651.2013.04.011 |
| 中文关键词: $\rho^*$-混合随机变量列 加权和 完全收敛性 矩不等式. |
| 英文关键词:$\rho^*$-mixing sequence of random variables weighted sums complete convergence moment inequality. |
| 基金项目:国家自然科学基金(Grant Nos.11271020; 11201004),教育部科学技术研究重点项目(Grant No.211077), 安徽省自然科学基金 (Grant Nos.10040606Q30; 1208085MA11). |
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| 中文摘要: |
| 本文研究了$\rho^*$-混合随机变量列加权和的完全收敛性. 通过运用矩不等式和截尾法, 建立了$\rho^*$-混合随机变量列加权和的完全收敛性的等价条件. 这些结果不仅将文献[7](J. Theoret. Probab.,1995,{\bf 8}(1):49-76)的结果从独立同分布推广至$\rho^*$-混合,而且获得了其必要性,并弱化了条件. |
| 英文摘要: |
| In this paper, the complete convergence of weighted sums for $\rho^*$-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for $\rho^*$-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, {\bf 8}(1): 49--76) from i.i.d. to $\rho^*$-mixing setting but also obtain their necessities and relax their conditions. |
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