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Title: Variance of periodic measure of bounded set with random position (English)
Author: Janáček, Jiří
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 47
Issue: 3
Year: 2006
Pages: 443-455
Category: math
Summary: The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in $\Bbb R^d$ under uniform random shift is proportional to the $(d+1)$st power of the grid scaling factor. This result remains valid for a bounded set in $\Bbb R^d$ with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to the $(d-1)$-dimensional measure of the object boundary. The related coefficients are calculated for various periodic grids constructed from affine sets. (English)
Keyword: periodic measure
Keyword: variance
MSC: 60E99
MSC: 62D05
MSC: 62E20
MSC: 62J10
idZBL: Zbl 1150.62315
idMR: MR2281006
Date available: 2009-05-05T16:58:33Z
Last updated: 2012-04-30
Stable URL:
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