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

2018/02/06 by Chen, Jia, Wang, Heping, Zhang, Jie
#41A25 #41A63 #65D15 #65Y20 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1802.01829

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∈(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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