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August, 1975 On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability"
P. Gacs, D. Szasz
Ann. Probab. 3(4): 597-607 (August, 1975). DOI: 10.1214/aop/1176996303

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.

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P. Gacs. D. Szasz. "On a Problem of Cox Concerning Point Processes in $R^k$ of "Controlled Variability"." Ann. Probab. 3 (4) 597 - 607, August, 1975. https://doi.org/10.1214/aop/1176996303

Information

Published: August, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0316.60037
MathSciNet: MR388536
Digital Object Identifier: 10.1214/aop/1176996303

Subjects:
Primary: 60D05
Secondary: 60K99

Keywords: Geometrical probability , random displacements , Stochastic point processes

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 4 • August, 1975
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