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

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 E n , a fixed n-dimensional convex body K 0 of volume V 0 and a system K 1,…,K m of mn-dimensional convex bodies, congruent to a convex set K. Assume that the sets K i (i = 1,…,m) have random positions, being stochastically independent and uniformly distributed on a limited domain of E n and denote by V m the volume of the convex body K m = K 0 ∩ (K 1 ∩ … ∩ K m ). The aim of this paper is the evaluation of the second moment of the random variable V m .

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

Information

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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