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首页> 外文期刊>Journal of complexity >Asymptotic analysis in multivariate average case approximation with Gaussian kernels
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Asymptotic analysis in multivariate average case approximation with Gaussian kernels

机译：Asymptotic analysis in multivariate average case approximation with Gaussian kernels

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We consider tensor product random fields Y-d, d is an element of N, whose covariance functions are Gaussian kernels with a given sequence of length scale parameters. We investigate the growth of the average case approximation complexity n(Yd)(epsilon) of Y-d for arbitrary fixed epsilon is an element of (0, 1) and d - infinity. Namely, we find criteria for the boundedness of n(Yd)(epsilon) depending on d and criteria for n(Yd)(epsilon) - infinity when d - infinity for any fixed epsilon is an element of(0, 1). In the latter case we obtain necessary and sufficient conditions for the following logarithmic asymptoticsln n(Yd) (epsilon) = a(d) + q(epsilon)b(d) + o(b(d)), d - infinity,with any epsilon is an element of (0, 1). Here q:(0, 1) - R is a non-decreasing function, (a(d))(d is an element of N) is a sequence and (b(d))(d is an element of N) is a positive sequence such that b(d) - infinity, d - infinity. We show that only special quantiles of self-decomposable distribution functions appear as functions q in a given asymptotics. These general results apply to n(Yd)(epsilon) under particular assumptions on the length scale parameters. (C) 2021 Elsevier Inc. All rights reserved.

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