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

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

2008-06-19

arxiv.org/abs/0806.3180v2

Advances in Applied Probability 41 (2009) 623-646

Mathematics

Probability

Accepted in Advances in Applied Probability. Propn. 3.2 strengthened and as a consequence Cor 6.1,6.2,6.3

Scientific paper

10.1239/aap/1253281057

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.

Affiliated with

Also associated with

No associations

Rating

Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-563000