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Piecewise multilinear interpolation of a random field
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
2013 (engelsk)Inngår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 45, nr 4, s. 945-959Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

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.

sted, utgiver, år, opplag, sider
2013. Vol. 45, nr 4, s. 945-959
Emneord [en]
Approximation, random field, piecewise-multilinear interpolator, sampling design
HSV kategori
Forskningsprogram
matematisk statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-81408DOI: 10.1239/aap/1386857852ISI: 000330201100004OAI: oai:DiVA.org:umu-81408DiVA, id: diva2:655037
Forskningsfinansiär
Swedish Research Council, 2009-4489Tilgjengelig fra: 2013-10-09 Laget: 2013-10-09 Sist oppdatert: 2018-06-08bibliografisk kontrollert

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