论文标题
在不可分割的Banach空间上的高斯随机字段
Gaussian random fields on non-separable Banach spaces
论文作者
论文摘要
我们在某些BANACH空间上研究高斯随机场，并研究其存在的条件。我们的结果除外，还适用于ra和hölder函数的空间。在前一种情况下，我们能够直接在度量的空间上定义高斯白噪声，例如避免将嵌入到负阶Sobolev空间中。在后一种情况下，我们演示了样品的Hölder规律性如何由协方差内核的控制，因此显示了与Kolmogorov-Chentsov定理的连接。
We study Gaussian random fields on certain Banach spaces and investigate conditions for their existence. Our results apply inter alia to spaces of Radon measures and Hölder functions. In the former case, we are able to define Gaussian white noise on the space of measures directly, avoiding, e.g., an embedding into a negative-order Sobolev space. In the latter case, we demonstrate how Hölder regularity of the samples is controlled by that of the covariance kernel and, thus, show a connection to the Theorem of Kolmogorov-Chentsov.
