论文标题
Wiener空间上的多元正常近似：凸距离的新边界
Multivariate normal approximation on the Wiener space: new bounds in the convex distance
论文作者
论文摘要
我们在高斯磁场平滑函数的矢量与具有正相协方差矩阵的正常矢量的矢量之间的分布之间建立了明确的界限。我们的边界与Nourdin，Peccati和Réveillac（2010）获得的（更平滑）1-Wasserstein距离所获得的边界相称，并且不涉及任何其他对数因子。我们工作中利用的主要工具之一是对Schulte和Yukich（2019）最近获得的凸距离的递归估计。我们在两种不同的情况下说明了我们的抽象结果：（i）我们证明了多个Wiener-Itô积分向量的定量多变量第四刻定理，（ii）我们表征了功能性breuer-major理论中有限维分布的收敛速率。
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the ones obtained by Nourdin, Peccati and Réveillac (2010) for the (smoother) 1-Wasserstein distance, and do not involve any additional logarithmic factor. One of the main tools exploited in our work is a recursive estimate on the convex distance recently obtained by Schulte and Yukich (2019). We illustrate our abstract results in two different situations: (i) we prove a quantitative multivariate fourth moment theorem for vectors of multiple Wiener-Itô integrals, and (ii) we characterise the rate of convergence for the finite-dimensional distributions in the functional Breuer-Major theorem.
