LIMIT LAWS FOR k-COVERAGE OF PATHS BY A MARKOV-POISSON-BOOLEAN MODEL

Abstract

Let P := {Xi}(i >= 1) be a stationary Poisson point process R-d, {C-i}(i >= 1) be a sequence of i.i.d. random sets in R-d, and {Y-t(i); t >= 0}(i >= 1) be i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the Markov-Poisson-Boolean model C-t :={Y-i(t) (X-i + C-i), i >= 1}. C-t represents the coverage process at time t. We first obtain limit laws for k-coverage of an area at an arbitrary instant. We then obtain the limit laws for the k-coverage seen by a particle as it moves along a one-dimensional path.