| 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:
|
http://hdl.handle.net/10338.dmlcz/119605 |
| . |
| Reference:
|
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| . |
