Geodesic
Russo's formula for Poisson point fields and its applications
Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 149-160
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove a new integral formula for Poisson point fields that is analogous to Russo's formula for Bernoulli fields. We use this formula to find the conditional distribution of the volume of the fundamental domain of the Voronoi mosaic that is generated by a homogeneous Poisson field of intensity $\lambda$ in $R^d$. Under the condition that the Voronoi polyhedron has $N$ hyperfaces, the volume of this domain has the gamma distribution $\Gamma (N,\lambda)$, which also provides an estimate for the distribution of the volume of a Voronoi polyhedron having $N$ hyperfaces. 
@article{DM_1992_4_3_a12,
     author = {S. A. Zuev},
     title = {Russo's formula for {Poisson} point fields and its applications},
     journal = {Diskretnaya Matematika},
     pages = {149--160},
     year = {1992},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_3_a12/}
}
TY  - JOUR
AU  - S. A. Zuev
TI  - Russo's formula for Poisson point fields and its applications
JO  - Diskretnaya Matematika
PY  - 1992
SP  - 149
EP  - 160
VL  - 4
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_1992_4_3_a12/
LA  - ru
ID  - DM_1992_4_3_a12
ER  - 
%0 Journal Article
%A S. A. Zuev
%T Russo's formula for Poisson point fields and its applications
%J Diskretnaya Matematika
%D 1992
%P 149-160
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1992_4_3_a12/
%G ru
%F DM_1992_4_3_a12
S. A. Zuev. Russo's formula for Poisson point fields and its applications. Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 149-160. http://geodesic.mathdoc.fr/item/DM_1992_4_3_a12/