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The variance of a Poisson process of domains

Published online by Cambridge University Press:  14 July 2016

A. M. Kellerer
A. M. Kellerer*
Affiliation:
University of Würzburg
*
∗Postal address: Institut für Med. Strahlenkunde der Universität Würzburg, Versbacher Str. 5, D-8700 Würzburg, W. Germany.
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Abstract

A familiar relation links the densities that result for the intersection of a convex body and straight lines under uniform isotropic randomness with those that result under weighted randomness. An extension of this relation to the intersection of more general domains is utilized to obtain the variance of the n-dimensional measure of the intersection of two bodies under uniform isotropic randomness. The formula for the variance contains the point-pair-distance distributions for the two domains — or the closely related geometric reduction factors. The result is applied to derive the variance of the intersection of a Boolean scheme, i.e. a stationary, isotropic Poisson process of domains, with a fixed sampling region.

Keywords

RANDOM INTERSECTION OF GEOMETRIC OBJECTSVARIANCE OF OVERLAPLATTICE PROBLEMPOISSON PROCESSBOOLEAN SCHEMEPOINT-PAIR-DISTANCE DISTRIBUTION
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 307 - 321
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Work supported by Euratom Contract BI-6-0013 D(B) and Contract 96731 with GSI (Gesellschaft für Schwerionenforschung, Darmstadt).

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