Coverage of space in Boolean models

Details Coverage of space in Boolean models Coverage of space in Boolean models

2006-08-10

arxiv.org/abs/math/0608238v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 119-127

Mathematics

Combinatorics

Published at http://dx.doi.org/10.1214/074921706000000158 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000158

For a marked point process $\{(x_i,S_i)_{i\geq 1}\}$ with $\{x_i\in \Lambda:i\geq 1\}$ being a point process on $\Lambda \subseteq \mathbb{R}^d$ and $\{S_i\subseteq R^d:i\geq 1\}$ being random sets consider the region $C=\cup_{i\geq 1}(x_i+S_i)$. This is the covered region obtained from the Boolean model $\{(x_i+S_i):i\geq 1\}$. The Boolean model is said to be completely covered if $\Lambda \subseteq C$ almost surely. If $\Lambda$ is an infinite set such that ${\bf s}+\Lambda \subseteq \Lambda$ for all ${\bf s}\in \Lambda$ (e.g. the orthant), then the Boolean model is said to be eventually covered if ${\bf t}+\Lambda \subseteq C$ for some ${\bf t}$ almost surely. We discuss the issues of coverage when $\Lambda$ is $\mathbb{R}^d$ and when $\Lambda$ is $[0,\infty)^d$.

Affiliated with

Also associated with

No associations

Rating

Coverage of space in Boolean models 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 Coverage of space in Boolean models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coverage of space in Boolean models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312127