Variance of periodic measure of bounded set with random position
نویسندگان
چکیده
The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in R 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 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.
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