Comparison of Moments of Sums of Independent Random Variables and Differential Inequalities
Comparison of Moments of Sums of Independent Random Variables and Differential Inequalities
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独立随机变量之和矩与微分不等式的比较
DOI：
10.1006/jfan.1996.0030
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发表时间：
1996
影响因子：
1.7
通讯作者：
K. Oleszkiewicz
中科院分区：
文献类型：
--
作者：
S. Kwapień;R. Latala;K. Oleszkiewicz
对于S =∑ xi <$i，其中（xi）是独立对称随机变量序列，（xi）是赋范空间中的向量序列，给出了不等式（E <$S <$p）1/p <$Cp，q（E <$S <$q）1/q的两种证明方法，其中常数Cp，q与序列（xi）无关.这些方法依赖于Poincare型或对数Sobolev型微分不等式。所得到的常数通常比用其他方法得到的常数好。
ForS=∑ xiξi, where (ξi) is a sequence of independent, symmetric random variables and (xi) is a sequence of vectors in a normed space we give two methods of proving inequalities (E ∥S∥p)1/p⩽Cp, q(E ∥S∥q)1/qwith the constantsCp, qindependent of the sequence (xi). The methods depend on using differential inequalities of Poincare or logarithmic Sobolev type. The obtained constants are usually better than the ones obtained by other methods.