Asymptotic analysis of average case approximation complexity of additive random fields
Abstract
We study approximation properties of sequences of centered additive random fields $Y_d$, $d\in\mathbb{N}$. The average case approximation complexity $n^{Y_d}(\varepsilon)$ is defined as the minimal number of evaluations of arbitrary linear functionals that is needed to approximate $Y_d$ with relative $2$average error not exceeding a given threshold $\varepsilon\in(0,1)$. We investigate the growth of $n^{Y_d}(\varepsilon)$ for arbitrary fixed $\varepsilon\in(0,1)$ and $d\to\infty$. Under natural assumptions we obtain general results concerning asymptotics of $n^{Y_d}(\varepsilon)$. We apply our results to additive random fields with marginal random processes corresponding to the Korobov kernels.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 DOI:
 10.48550/arXiv.1710.10865
 arXiv:
 arXiv:1710.10865
 Bibcode:
 2017arXiv171010865K
 Keywords:

 Mathematics  Probability