The Annals of Probability

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

P. Gacs and D. Szasz

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60K99: None of the above, but in this section

Keywords
Stochastic point processes random displacements geometrical probability

Citation

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


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