论文标题
通过Skorohod估算和$ p $-Poincaré不平等的定量CLT在泊松空间上
Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincaré inequalities
论文作者
论文摘要
我们基于Skorohod积分矩的新估计值对泊松功能的高斯近似建立了新的明确界限。将它们与Malliavin-Stein方法相结合，我们在Wasserstein和Kolmogorov距离中得出了边界，它们的应用需要对附加成本运算符$ \ Unicode $ \ Unicode {x2014} $的最小矩假设，从而扩大了结果（上次，Peccati和Schulte，2016年）。我们的应用程序包括用于在线最近的邻居图的CLT，其有效性是在（Wade，2009; Penrose and Wade，2009年）中的。我们还将技术应用于吉尔伯特图的边缘功能，$ k $ near的邻居图和径向生成树的质量clts，如果在定性clt是已知且未知的情况下。
We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires minimal moment assumptions on add-one cost operators $\unicode{x2014}$ thereby extending the results from (Last, Peccati and Schulte, 2016). Our applications include a CLT for the Online Nearest Neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the $k$-Nearest Neighbour graph and of the Radial Spanning Tree, both in cases where qualitative CLTs are known and unknown.
