论文标题
关于零均值高斯措施的正交性：足够致密的采样
On the orthogonality of zero-mean Gaussian measures: Sufficiently dense sampling
论文作者
论文摘要
对于一个固定的随机函数$ξ$，在子集$ d $ of $ \ mathbb {r}^{d} $上进行采样，我们检查了两个零均值高斯度量的等价和正交性$ \ mathbb {p} _ {1} _ {1} $ and $ \ \ \ \ \ \ \ \ p} $ {2} $ {2} $ {2} $ {2} $ {2}我们给出了各向同性类似物的结果，即$ \ mathbb {p} _ {1} $和$ \ mathbb {p} _ {2} $的等效性与存在$ \ mathbbbbbbbbbbbbbbbb {p} $ {p} $ {p} $ {1} $ {1} $ and的差差的方面扩展的存在链接在一起。 $ \ mathbb {p} _ {2} $从$ d $到$ \ mathbb {r}^{d} $。我们表明，当$ \ mathbb {p} _ {1} $和$ \ mathbb {p} _ {2} $的正交性可以恢复。
For a stationary random function $ξ$, sampled on a subset $D$ of $\mathbb{R}^{d}$, we examine the equivalence and orthogonality of two zero-mean Gaussian measures $\mathbb{P}_{1}$ and $\mathbb{P}_{2}$ associated with $ξ$. We give the isotropic analog to the result that the equivalence of $\mathbb{P}_{1}$ and $\mathbb{P}_{2}$ is linked with the existence of a square-integrable extension of the difference between the covariance functions of $\mathbb{P}_{1}$ and $\mathbb{P}_{2}$ from $D$ to $\mathbb{R}^{d}$. We show that the orthogonality of $\mathbb{P}_{1}$ and $\mathbb{P}_{2}$ can be recovered when the set of distances from points of $D$ to the origin is dense in the set of non-negative real numbers.
