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arXiv · 1802.01829

Average Case $(s, t)$-weak tractability of non-homogenous tensor product problems

Jia Chen·Heping Wang·Jie Zhang
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Abstract

We study $d$-variate problem in the average case setting with respect to a zero-mean Gaussian measure. The covariance kernel of this Gaussian measure is a product of univariate kernels and satisfies some special properties. We study $(s, t)$-weak tractability of this multivariate problem, and obtain a necessary and sufficient condition for $s>0$ and $t\in(0,1)$. Our result can apply to the problems with covariance kernels corresponding to Euler and Wiener integrated processes, Korobov kernels, and analytic Korobov kernels.

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Jia Chen, Heping Wang, Jie Zhang. 2018-02-06. Average Case $(s, t)$-weak tractability of non-homogenous tensor product problems. https://arxiv.org/abs/1802.01829

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