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Piecewise-Multilinear Interpolation of a Random Field

Part of: Approximations and expansions Stochastic processes

Published online by Cambridge University Press:  04 January 2016

Konrad Abramowicz  and
Oleg Seleznjev
Konrad Abramowicz*
Affiliation:
Umeå University
Oleg Seleznjev*
Affiliation:
Umeå University
*
∗ Postal address: Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden.
∗ Postal address: Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden.
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Abstract

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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.

Keywords

Approximationrandom fieldpiecewise-multilinear interpolatorsampling design

MSC classification

Primary: 60G60: Random fields
Secondary: 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section) 41A05: Interpolation
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 4 , December 2013 , pp. 945 - 959
Copyright
© Applied Probability Trust 

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