论文标题
关于$ d $二维的融合的说明
A note on convergence in mean for $d$-dimensional arrays of random vectors in Hilbert spaces under the Cesàro uniform integrability
论文作者
论文摘要
本说明以$ p $的平均值，$ 0 <p \ le 1 $建立融合，对于$ d $二维的二等数阵列，在cesàro统一的集成性条件下，希尔伯特空间中的随机向量阵列。在$ 0 <p <1 $的情况下，我们的$ L_P $ Convergence都是有效的，无论依赖性结构如何。在$ p = 1 $的情况下，基础随机向量应该是成对独立的。为最大部分总和建立了平均收敛结果，而以前的贡献仅被视为部分总和。文献中的一些结果扩大了。还详细介绍了$ d $二维阵列的CESàRO统一集成性的各种特性，例如经典等效标准和DelaValléePoussin定理。
This note establishes convergence in mean of order $p$, $0<p\le 1$ for $d$-dimensional arrays of random vectors in Hilbert spaces under the Cesàro uniform integrability conditions. In the case where $0<p<1$, our $L_p$ convergence is valid irrespective of any dependence structure. In the case where $p=1$, the underlying random vectors are supposed to be pairwise independent. The mean convergence results are established for maximal partial sums while previous contributions were so far considered partial sums only. Some results in the literature are extended. Various properties of the Cesàro uniform integrability of $d$-dimensional arrays of random vectors such as the classical equivalent criterion and the de La Vallée Poussin theorem are also detailed.
