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December 2013 Piecewise-multilinear interpolation of a random field
Konrad Abramowicz, Oleg Seleznjev
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Adv. in Appl. Probab. 45(4): 945-959 (December 2013). DOI: 10.1239/aap/1386857852

Abstract

We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

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Konrad Abramowicz. Oleg Seleznjev. "Piecewise-multilinear interpolation of a random field." Adv. in Appl. Probab. 45 (4) 945 - 959, December 2013. https://doi.org/10.1239/aap/1386857852

Information

Published: December 2013
First available in Project Euclid: 12 December 2013

zbMATH: 1354.60056
MathSciNet: MR3161291
Digital Object Identifier: 10.1239/aap/1386857852

Subjects:
Primary: 60G60
Secondary: 41A05, 41A63

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 4 • December 2013
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