论文标题
较强依赖矢量随机场的功能的还原原理
Reduction principle for functionals of strong-weak dependent vector random fields
论文作者
论文摘要
我们证明了具有弱且强烈依赖组件的矢量随机场功能的渐近原理。这些功能可用于构建具有偏斜和重尾分布的新类别随机字段。与标量远程依赖的随机场的情况相反，这表明此类功能的渐近行为不一定取决于其Hermite等级的术语。结果通过应用于学生随机字段的第一个Minkowski功能的应用来说明结果。还提出了一些基于理论发现的仿真研究。
We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed distributions. Contrary to the case of scalar long-range dependent random fields, it is shown that the asymptotic behaviour of such functionals is not necessarily determined by the terms at their Hermite rank. The results are illustrated by an application to the first Minkowski functional of the Student random fields. Some simulation studies based on the theoretical findings are also presented.
