We derive and discuss formulas for the density and the hazard rate of the empty space function of a germ-grain model in R d generated by a stationary point process and i.i.d. convex primary grains n , n 2 N, that are independent of. Our formulas are based on the Palm probability of the germ process and the mean generalized curvature measure of the grain. Particular attention is paid to cluster ...

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a non-homogeneous Poisson process, and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Po...

Abstract This paper examines methodologies for the simulation of storms for the purpose of design flood generation in the Thames region. Existing methods are reviewed and two new approaches are proposed. One combines point profiles of storms extracted from long rainfall records with depth-duration-frequency statistics. The other uses a stochastic rainfall model based upon the Poisson point proc...

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach, combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard ...

The correlation structure of some remarkable point processes on the onedimensional real line is investigated. More specifically, focus is on translation invariant determinantal, permanental and/or renewal point processes. In some cases, anomalous (non-Poissonian) fluctuations for the number of points in a large window can be observed. This may be read from the total correlation function of the ...

A Poisson process in space{time is used to generate a linear Kolmogorov's birth{growth model. Points start to form on 0; L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of 0; L]. The whole interval will eventually be passed over by moving frontiers. Let N L be the total number of po...

We consider a spatial stochastic model of wireless cellular networks, where the base stations (BSs) are deployed according to a simple and stationary point process on R, d ≥ 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio (SIR), which is a key quantity in wireless communications. In the case where the path-loss function representing signal a...

Sampling from a random discrete distribution induced by a ‘stick-breaking’ process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the halfline.