Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications

Bartlomiej Blaszczyszyn 1 D. Yogeshwaran 1, *
* Auteur correspondant
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt
Abstract : Directionally convex ($dcx$) ordering is a tool for comparison of dependence structure of random vectors that also takes into account the variability of the marginal distributions. When extended to random fields it concerns comparison of all finite dimensional distributions. Viewing locally finite measures as non-negative fields of measure-values indexed by the bounded Borel subsets of the space, in this paper we formulate and study the $dcx$ ordering of random measures on locally compact spaces. We show that the $dcx$ order is preserved under some of the natural operations considered on random measures and point processes, such as deterministic displacement of points, independent superposition and thinning as well as independent, identically distributed marking. Further operations such as position dependent marking and displacement of points though do not preserve the $dcx$ order on all point processes, are shown to preserve the order on Cox point processes. We also examine the impact of $dcx$ order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions, pair correlation functions as well as examples seem to indicate that point processes higher in $dcx$ order cluster more. As the main result, we show that non-negative integral shot-noise fields with respect to $dcx$ ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot-noise fields appear as key ingredients. We also mention a few pertinent open questions.
Type de document :
Article dans une revue
Advances in Applied Probability, Applied Probability Trust, 2009, 41, pp.623-646. 〈10.1239/aap/1253281057〉
Liste complète des métadonnées

https://hal.inria.fr/inria-00288866
Contributeur : D. Yogeshwaran <>
Soumis le : jeudi 2 avril 2009 - 02:11:31
Dernière modification le : jeudi 11 janvier 2018 - 06:20:06
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 11:54:41

Fichiers

SNORDER_rev2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Bartlomiej Blaszczyszyn, D. Yogeshwaran. Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications. Advances in Applied Probability, Applied Probability Trust, 2009, 41, pp.623-646. 〈10.1239/aap/1253281057〉. 〈inria-00288866v2〉

Partager

Métriques

Consultations de la notice

322

Téléchargements de fichiers

159