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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

[1] Chern, S. S. and Yien, Ch. T. (1940). Sulla formula principale cinematica dello spazio ad n dimensioni. Bol. Un. Mat. Italiana 2, 434–437.Google Scholar
[2] Hadwiger, H. (1950). Neue Integralrelationen für Eikörperpaare. Acta Scientiarum Mathematicarum 13, 252–257.Google Scholar
[3] Santaló, L. A. (1976). Integral Geometry and Geometric Probability. Addison-Wesley.Google Scholar
[4] Stoka, M. I. (1972). Sur quelques variances attachées aux systèmes d'ovales. Pub. Inst. Stat. Univ. Paris XXI 3–4, 71–76.Google Scholar
[5] Stoka, M. I. (1973–1974). Sur quelques problèmes de géométrie intégrale dans l'espace euclidien En . Atti Accad. Sci. Torino 108, 183–193.Google Scholar
[6] Stoka, M. I. (1974). Une extension du problème de l'aiguille de Buffon dans l'espace euclidien Rn . Bol. Un. Mat. Italiana 10, 386–389.Google Scholar
[7] Stoka, M. I. (1977). Sur les variances attachées aux quelques familles d'ovaloides dans l'espace R3 . Pub. Inst. Stat. Univ. Paris XXII 3–4, 99–105.Google Scholar