Variance of periodic measure of bounded set with random position

Jiří Janáček

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 443-455
  • ISSN: 0010-2628

Abstract

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The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in 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 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.

How to cite

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Janáček, Jiří. "Variance of periodic measure of bounded set with random position." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 443-455. <http://eudml.org/doc/249875>.

@article{Janáček2006,
abstract = {The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in $\mathbb \{R\}^d$ 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 $\mathbb \{R\}^d$ 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.},
author = {Janáček, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {periodic measure; variance},
language = {eng},
number = {3},
pages = {443-455},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Variance of periodic measure of bounded set with random position},
url = {http://eudml.org/doc/249875},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Janáček, Jiří
TI - Variance of periodic measure of bounded set with random position
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 443
EP - 455
AB - The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in $\mathbb {R}^d$ 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 $\mathbb {R}^d$ 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.
LA - eng
KW - periodic measure; variance
UR - http://eudml.org/doc/249875
ER -

References

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