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On a random variable related to a system of convex bodies in the Euclidean space En

Part of: Geometric probability and stochastic geometry General convexity

Published online by Cambridge University Press:  01 July 2016

Marius Stoka
Marius Stoka*
Affiliation:
Università di Torino
*
∗ Postal address: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I 10123 Torino, Italy.
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Abstract

Let us consider, in the Euclidean space En, a fixed n-dimensional convex body K0 of volume V0 and a system K1,…,Km of mn-dimensional convex bodies, congruent to a convex set K. Assume that the sets Ki (i = 1,…,m) have random positions, being stochastically independent and uniformly distributed on a limited domain of En and denote by Vm the volume of the convex body Km = K0 ∩ (K1 ∩ … ∩ Km). The aim of this paper is the evaluation of the second moment of the random variable Vm.

Keywords

Geometric probabilitystochastic geometryrandom setsrandom convex sets and integral geometry

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 335 - 341
Copyright
Copyright © Applied Probability Trust 1998 

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References

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