论文标题
泊松功能方差的下限
Lower bounds for variances of Poisson functionals
论文作者
论文摘要
通常需要进行方差的下限来得出中心极限定理。在本文中，我们为使用malliavin conculus的差异操作员的泊松功能方差建立了一个下限。泊松功能，即取决于泊松过程的随机变量，经常以随机几何形状进行研究。我们将较低的方差绑定到空间随机图的统计数据，$ l^p $表面积和随机多型的表面积以及泊松射击噪声过程的游览集量。因此，我们不仅结合了下面的差异，而且还显示出渐近协方差矩阵的正面确定性，并为多元正常近似值提供相关的结果。
Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the difference operator of Malliavin calculus. Poisson functionals, i.e. random variables that depend on a Poisson process, are frequently studied in stochastic geometry. We apply our lower variance bound to statistics of spatial random graphs, the $L^p$ surface area of random polytopes and the volume of excursion sets of Poisson shot noise processes. Thereby we do not only bound variances from below but also show positive definiteness of asymptotic covariance matrices and provide associated results on the multivariate normal approximation.
