On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_3$

Caristi, Giuseppe; Molica Bisci, Giovanni

On the Variance Associated to a Family of Ovaloids in the Euclidean Space

E_{3}

Caristi, Giuseppe ; Molica Bisci, Giovanni

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 87-98 / Harvested from Biblioteca Digitale Italiana di Matematica

Access to full text
Full (PDF)
Full (DjVu)

Abstract
Résumé

In this paper we consider a random variable $h$ arising from an intersection problem between a fixed convex body $K_{0}$ and a system of random independent and uniformly distributed ovaloids in $E_{3}$ .

In questo lavoro si cosidera una variabile aleatoria $h$ associata a un sistema di ovaloidi indipendenti e uniformemente distribuiti nello spazio Euclideo tridimensionale ed a un fissato corpo convesso $K_{0}$ .

Publié le : 2007-02-01

MR 2310960 | Zbl 1129.60013

@article{BUMI_2007_8_10B_1_87_0,
     author = {Giuseppe Caristi and Giovanni Molica Bisci},
     title = {On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E\_3$},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {87-98},
     zbl = {1129.60013},
     mrnumber = {2310960},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_1_87_0}
}

Caristi, Giuseppe; Molica Bisci, Giovanni. On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_3$. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 87-98. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_1_87_0/

Bibliographie

[1] Blaschke, W., Vorlesungen über Integralgeometrie, III Auflage, V.E.B. Deutscher Verlag der Wiss., Berlin (1955). | MR 76373

[2] Czuber, E., Zur Theorie der geometrischen Wahrscheinlichketein, Sitz. Akad. Wiss. Wien, 90 (1884), 719-742. | Zbl 16.0180.01

[3] Molica Bisci, G., Random systems of planes in the Euclidean Space $E_{3}$ , Atti Acc. Scienze di Torino (2005). | MR 2256681

[4] Poincaré, H., Calcul des probabilitiés, ed. 2, Carré, Paris, 1912. | Zbl 43.0308.04

[5] Santaló, L. A., Über das Kinematische Mass in Raum, Bull. Act. Sci. et Ind., n. 357, Hermann, Paris, (1936).

[6] Stoka, M., La variance d'une variable aléatoire associée a une famille des ovales du plan euclidien, Bull. Ac. royale de Belgique (1973). | MR 322765

[7] Stoka, M., Sur les variances attachees aux quelques familles d'ovaloides dans l'espace $E_{3}$ , Pubb. Inst. Stat. Univ. Paris, 3-4 (1977), 99-105. | MR 488216