Limit Laws fork-Coverage of Paths by a Markov–Poisson–Boolean Model
Srikanth K. Iyer, Deepika Revankar Manjunath, Dhandapani Yogeshwaran · Stochastic Models · 2008
Let P: = {X i } i≥1 be a stationary Poisson point process in ℜ d , {C i } i≥1 be a sequence of i.i.d. random sets in ℜ d , and be i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the Markov–Poisson–Boolean model . 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.