Logo
EnglishCookie löschen - von nun an wird die Spracheinstellung Ihres Browsers verwendet.
Kellerer, Albrecht M. (1986): The variance of a poisson process of domains. In: Journal of applied probability, Vol. 23: S. 307-321
[img]
Vorschau

PDF

1MB

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.