Excursions of random fields with long range dependence

具有长程依赖性的随机场偏移

• 批准号: 390879134
• 负责人: Professor Dr. Evgeny Spodarev
• 金额: --
• 依托单位: Institut für Stochastik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/390879134?language=en
• 关键词: Excursions; random; fields; long; range

In the prolongation project we would like to determine the limiting behaviour of volumes of excursion sets of non-Gaussian subordinated random fields with long-range dependence. First, we consider the case when bivariate densities of the field have a certain diagonal expansion w.r.t an orthonormal complete system of polynomials. E.g., isotropic Gamma-marginally-distributed random fields will need Laguerre polynomials here. Second, we would like to determine the limiting behaviour of level sets' volumes for SαS moving average random fields under long memory. Third, we would like to find conditions on the kernel function when a continuous infinitely divisible moving average random field has short or long-range dependence in the sense of Definition of Kulik & Spodarev (2021) which involves volumes of their level sets.

在延拓工程中，我们想确定具有长程相关性的非高斯从属随机场的偏移集的体积的极限行为。首先，我们考虑的情况下，当双变量密度的字段有一定的对角展开w.r.t的正交完全系统的多项式。例如，在一个示例中，各向同性伽玛边缘分布随机场在这里需要拉盖尔多项式。其次，我们想确定长记忆下SαS滑动平均随机场水平集体积的极限行为。第三，我们想找到核函数的条件，当一个连续的无限可分移动平均随机场具有Kulik & Spodarev（2021）定义意义上的短程或长程依赖性时，这涉及到它们水平集的体积。