Showing papers on "Subordinator published in 1985"
TL;DR: In this paper, the uncovered set is a regenerative set in the sense of Hoffmann-Jorgensen's generalization of regenerative phenomena introduced by Kingman, and it is the closure of the image of a subordinator.
Abstract: Random covering intervals are placed on the real line in a Poisson manner. Lebesgue measure governs their (random) locations and an arbitrary measure μ governs their (random) lengths. The uncovered set is a regenerative set in the sense of Hoffmann-Jorgensen's generalization of regenerative phenomena introduced by Kingman. Thus, as has previously been obtained by Mandelbrot, it is the closure of the image of a subordinator —one that is identified explicitly. Well-known facts about subordinators give Shepp's necessary and sufficient condition on μ for complete coverage and, when the coverage is not complete, a formula for the Hausdorff dimension of the uncovered set. The method does not seem to be applicable when the covering is not done in a Poisson manner or if the line is replaced by the plane or higher dimensional space.
57 citations
01 Jan 1985
TL;DR: In this paper, it was shown that any such process is a randomly time-transformed compound Poisson process having a negative linear drift, and this connection was exploited to obtain limit theorems for the population size and for the jump times in the rabies model.
Abstract: It is known that Bartoszyiiski's model for the growth of rabies virus in an infected host is a continuous branching process. We show by explicit construction that any such process is a randomly time-transformed compound Poisson process having a negative linear drift. This connection is exploited to obtain limit theorems for the population size and for the jump times in the rabies model. Some of these results are obtained in a more general context wherein the compound Poisson process is replaced by a subordinator.
1 citations