## The Annals of Probability

### On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability"

#### Abstract

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.

#### Article information

Source
Ann. Probab. Volume 3, Number 4 (1975), 597-607.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996303

Digital Object Identifier
doi:10.1214/aop/1176996303

Mathematical Reviews number (MathSciNet)
MR388536

Zentralblatt MATH identifier
0316.60037

JSTOR
Gacs, P.; Szasz, D. On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability". Ann. Probab. 3 (1975), no. 4, 597--607. doi:10.1214/aop/1176996303. https://projecteuclid.org/euclid.aop/1176996303