On a Voronoi Aggregative Process Related to a Bivariate Poisson Process (1996)
| Venue: | Adv. in Appl. Probab |
| Citations: | 24 - 4 self |
BibTeX
@INPROCEEDINGS{Foss96ona,
author = {S. G. Foss and S. A. Zuyev},
title = {On a Voronoi Aggregative Process Related to a Bivariate Poisson Process},
booktitle = {Adv. in Appl. Probab},
year = {1996},
pages = {965--981}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.
Citations
| 362 | An Introduction to the Theory of Point Processes - Daley, Vere-Jones - 1988 |
| 231 | Stochastic Geometry and its Applications - Stoyan, Kendall, et al. - 1995 |
| 19 | Random subdivisions of space into crystals - Gilbert - 1962 |
| 4 | Estimates for distributions of the Voronoi polygon's geometric characteristics. Random Structures and Algorithms - Zuyev - 1992 |
| 2 | On a certain segment process with Voronoi Clustering - Foss - 1993 |
| 1 | G#om#trie al#atoire et archit#cture de r#seaux de t#l#communications - Baccelli, Klein, et al. - 1995 |
| 1 | Optimal network structure with randomly distributed nodes - Sallai - 1988 |
