论文标题
轴向对称高斯流程的Karhunen-Loève扩展：建模策略和$ l^2 $近似
Karhunen-Loève Expansions for Axially Symmetric Gaussian Processes: Modeling Strategies and $L^2$ Approximations
论文作者
论文摘要
球体上的轴向对称过程，为此，二阶依赖性结构可能会随纬度的变化而大不相同，它是建模位于地球大部分大部分的自然变量的空间不确定性的突出替代方案。在本文中，我们着重于轴向对称高斯过程的Karhunen-Loève扩展。首先，我们研究了Karhunen-Loève系数的参数家族，该系数允许多功能空间协方差函数。各向同性以及纵向独立性可以作为我们提议的极限案例获得。其次，我们介绍了一种使任何纵向可逆的过程不可逆的策略，这意味着其协方差函数可以接收沿纵向的某些类型的不对称性。然后，有限截断的karhunen-loève扩展用于近似轴向对称过程。对于此类近似值，提供了$ l^2 $ -Error的界限。进行数值实验以说明我们的发现。
Axially symmetric processes on spheres, for which the second-order dependency structure may substantially vary with shifts in latitude, are a prominent alternative to model the spatial uncertainty of natural variables located over large portions of the Earth. In this paper, we focus on Karhunen-Loève expansions of axially symmetric Gaussian processes. First, we investigate a parametric family of Karhunen-Loève coefficients that allows for versatile spatial covariance functions. The isotropy as well as the longitudinal independence can be obtained as limit cases of our proposal. Second, we introduce a strategy to render any longitudinally reversible process irreversible, which means that its covariance function could admit certain types of asymmetries along longitudes. Then, finitely truncated Karhunen-Loève expansions are used to approximate axially symmetric processes. For such approximations, bounds for the $L^2$-error are provided. Numerical experiments are conducted to illustrate our findings.
