欧拉和维纳综合过程多变量逼近问题的可操作性

Axioms Pub Date : 2024-05-15 DOI:10.3390/axioms13050326
Jie Zhang
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摘要

本文研究了在平均情况下,零均值高斯量的归一化误差准则下多元近似问题的可操作性。高斯度量与协方差核相关联,协方差核由一维核的张量乘积表示,一维核对应于具有非负和非递减平稳性参数 {rd}d∈N 的欧拉和维纳积分过程。除了 (s, 0)-WT 外,我们从正则性参数的渐近特性出发,给出了各种可操作性概念的匹配充分条件和必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tractability of Multivariate Approximation Problem on Euler and Wiener Integrated Processes
This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is represented by the tensor product of one-dimensional kernels corresponding to Euler and Wiener integrated processes with non-negative and nondecreasing smoothness parameters {rd}d∈N. We give matching sufficient and necessary conditions for various concepts of tractability in terms of the asymptotic properties of the regularity parameters, except for (s, 0)-WT.
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