Suppose that the $k$-dimensional lattice points are displaced independently of each other with the same probability distribution. Denote by $\operatorname{Var} N(A)$ the variance of the number of displaced points contained in the set $A$. The asymptotic behaviour of $\operatorname{Var} N(A)$ is determined for large convex $A$'s.
Publié le : 1975-08-14
Classification:
Stochastic point processes,
random displacements,
geometrical probability,
60D05,
60K99
@article{1176996303,
author = {Gacs, P. and Szasz, D.},
title = {On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability"},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 597-607},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996303}
}
Gacs, P.; Szasz, D. On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability". Ann. Probab., Tome 3 (1975) no. 6, pp. 597-607. http://gdmltest.u-ga.fr/item/1176996303/