论文标题
关于高斯次级Lévy领域的属性和应用
On properties and applications of Gaussian subordinated Lévy fields
论文作者
论文摘要
我们考虑通过将高斯随机场在某些空间域$ \ mathcal {d} \ subset \ subset \ mathbb {r}^d $，$ d $，$ d $，$ d \ geq 1 $ $ \ geq 1 $上服从高斯属于Lévy领域（GSLFS）。所得的随机场在分布上是柔性的，并且具有一般不连续的样本路径。对随机场的理论研究包括侧面分布，可能的近似值及其协方差函数。作为应用，考虑了一个随机椭圆PDE，其中构造的随机场发生在扩散系数中。此外，我们提出了各种数值示例，以说明我们的理论发现。
We consider Gaussian subordinated Lévy fields (GSLFs) that arise by subordinating Lévy processes with positive transformations of Gaussian random fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. The resulting random fields are distributionally flexible and have in general discontinuous sample paths. Theoretical investigations of the random fields include pointwise distributions, possible approximations and their covariance function. As an application, a random elliptic PDE is considered, where the constructed random fields occur in the diffusion coefficient. Further, we present various numerical examples to illustrate our theoretical findings.
