Consider the Boolean model in IR, where the germs form a homogeneous Poisson point process with intensity λ and the grains are convex compact random sets. It is known (see e.g. Section 9.5.3 in Cressie (1993)) that Laslett’s rule transforms the exposed tangent points of the Boolean model into a homogeneous Poisson process with the same intensity λ. In the present paper, we give a simple proof o...

We give formulae for diierent types of contact distribution functions for stationary (not necessarily Poisson) Voronoi tessellations in R d in terms of the Palm void probabilities of the generating point process. Moreover, using the well-known relationship between the linear contact distribution and the chord length distribution we derive a closed form expression for the mean chord length in te...

In [1], a new coverage process was defined. It was motivated by the various SINR(Signal to Interference Noise Ratio) models in wireless communications. The underlying point process was assumed to be a Poisson process. In this report, we extend the theory to the case when the underlying point process is a Poisson-Poisson cluster process. Firstly, we define the stochastic geometric model. We give...

Queueing systems which map Poisson input processes to Poisson output processes have been well-studied in classical queueing theory. This paper considers two discretetime queues whose analogs in continuous-time possess the Poisson-in-Poisson-out property. It is shown that when packets arriving according to an arbitrary ergodic stationary arrival process are passed through these queueing systems,...

The work described in this paper explores the use of Poisson point processes and stochastic arithmetic to perform signal processing functions. Our work is inspired by the asynchrony and fault tolerance of biological neural systems. The essence of our approach is to code the input signal as the rate parameter of a Poisson point process, perform stochastic computing operations on the signal in th...

We study the general problem of estimating a ‘hidden’ point process X given the realisation of an ‘observed’ point process Y (possibly defined in different spaces) with known joint distribution. We characterise the posterior distribution of X under marginal Poisson and Gauss-Poisson prior and when the transformation from X to Y includes thinning, displacement and augmentation with extra points....

In this article, we deal with a class of discrete-time reliability models. The failures are assumed to be generated by an underlying time inhomogeneous Markov chain. The multivariate point process of failures is proved to converge to a Poissontype process when the failures are rare. As a result, we obtain a Compound Poisson approximation of the cumulative number of failures. A rate of convergen...

Based on Stein’s method, we derive upper bounds for Poisson process approximation in the L1-Wasserstein metric d (p) 2 , which is based on a slightly adapted Lp-Wasserstein metric between point measures. For the case p = 1, this construction yields the metric d2 introduced in [Barbour, A. D. and Brown, T. C. (1992), Stochastic Process. Appl. 43(1), pp. 9–31], for which Poisson process approxima...

We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk-factors is available at the individual level for cases, but only at a spatially aggregated level...