论文标题
通过球形对称性的多维概率不平等
Multidimensional probability inequalities via spherical symmetry
论文作者
论文摘要
球形对称性论点用于生产一般的设备，以转换身份和不平等现象，以$ p $ p $ p $ th的实现随机变量的绝对矩转换为希尔伯特空间中随机矢量规范的相应身份的相应身份和不等式的不等式。特定结果包括以下内容：（i）在$ x $的特征功能方面，这种随机向量$ x $的$ p $ th时刻的表达； （ii）对现实评估的随机变量的先前获得的von〜bahr的扩展，具有最佳的恒定因子对希尔伯特空间中随机矢量的最佳恒定因子的扩展，但仍具有最佳的常数因子； （iii）在“人群之间的对比”和“种群之间的对比度之间”与希尔伯特空间中的随机向量之间的不平等量扩展。
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments of the norms of random vectors in Hilbert spaces. Particular results include the following: (i) an expression of the $p$th moment of the norm of such a random vector $X$ in terms of the characteristic functional of $X$; (ii) an extension of a previously obtained von~Bahr--Esseen-type inequality for real-valued random variables with the best possible constant factor to random vectors in Hilbert spaces, still with the best possible constant factor; (iii) an extension of a previously obtained inequality between measures of "contrast between populations" and "spread within populations" to random vectors in Hilbert spaces.
