论文标题
重尾移动平均值的多维正常近似
Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages
论文作者
论文摘要
在本文中，我们将Poisson功能的精致二阶不平等扩展到了一维的多维环境。它的证明基于Malliavin-Stein方法的多元版本，用于泊松空间上的正常近似。我们还提出了重型移动平均值的矢量值功能的部分资金的应用。该扩展允许具有多元参数的功能，即多个移动平均值以及功能的多元值。以前，在稳定移动平均过程的框架内尚未探讨这样的设置。它可以潜在地捕获仅一维边际无法描述的概率特性，而是需要联合分布。
In this paper we extend the refined second-order Poincaré inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal approximation on Poisson spaces. We also present an application to partial sums of vector-valued functionals of heavy-tailed moving averages. The extension allows a functional with multivariate arguments, i.e. multiple moving averages and also multivariate values of the functional. Such a set-up has previously not been explored in the framework of stable moving average processes. It can potentially capture probabilistic properties which cannot be described solely by the one-dimensional marginals, but instead require the joint distribution.
