Limit laws for k-coverage of paths by a Markov-Boolean model
Srikanth K. Iyer, Deepika Revankar Manjunath, Dhandapani Yogeshwaran · arXiv (Cornell University) · 2007
Let P: = {Xi}i≥1 be a stationary point process in ℜ d, {Ci}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-Boolean model Ct: = {Y t i (Xi + Ci), i ≥ 1}. Ct represents the coverage process at time t. We first obtain limit laws for k-coverage of an area at an arbitrary instant. We then derive limit laws for the k-coverage induced on a one-dimensional path at an arbitrary instant. Finally, we obtain the limit laws for the k-coverage seen by a particle as it moves along a one-dimensional path.