Excursions of random fields with long range dependence

在延拓项目中，我们想要确定具有长程相关性的非高斯从属随机场的游移集体积的极限行为。首先，我们考虑了当场的二元密度具有一定的对角展开式时的情形，即一个多项式的正交化完备系。例如，各向同性伽马边缘分布的随机场在这里将需要拉盖尔多项式。其次，我们确定了SαS滑动平均随机场在长记忆条件下水平集体积的极限行为。第三，在Kulik&Spodarev(2021)的定义下，当连续无限可分移动平均随机场具有短程或长程相关性时，我们想找到核函数的条件，该定义涉及其水平集的体积。

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.