One of the most well known examples of phenomena that introduces and motivates the study of continuum percolation is the process of the ground getting wet during a period of rain. At each point hit by a raindrop, one sees a circular wet patch. Right after the rain begins to fall what one sees is a small wet region inside a large dry region. At some instant, so many raindrops have hit the ground...

This paper studies the application of network non-orthogonal multiple access (N-NOMA) to vehicular communication networks, modeled by a Poisson line Cox point process (PLC). Particularly, road infrastructure is (PLP), whereas base stations (BSs) and users are located according 1D homogeneous processes (HPPPs) on each road. In considered N-NOMA scheme, there two types users, i.e., coordinated mu...

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process ...

This article employs the relation between probabilities of two consecutive values a Poisson random variable to derive conditions for weak convergence point processes process. As applications, we consider starting points k -runs in sequence Bernoulli variables, constructed using inradii and circumscribed radii inhomogeneous Poisson–Voronoi tessellations large nearest neighbor distances Boolean m...

We translate in semigroup theory our result Léandre, 1990 giving a necessary condition so that the law of a Markov process with jumps could have a strictly positive density. This result express, that we have to jump in a finite number of jumps in a “submersive” way from the starting point x to the end point y if the density of the jump process p1 x, z is strictly positive in x, y . We use theMa...

A range of point process models which are commonly used in spatial epidemiology applications for the increased incidence of disease are compared. The models considered vary from approximate methods to an exact method. The approximate methods include the Poisson process model and methods that are based on discretization of the study window. The exact method includes a marked point process model,...

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The tem...

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The tem...

The use of properties of a Poisson process to study the randomness of stars is traced back to a 1767 paper. The process was used and rediscovered many times, and we mention some of the early scientific areas. The name Poisson process was first used in print in 1940, and we believe the term was coined in the corridors of Stockholm University some time between 1936 and 1939. We follow the early d...

The estimation of the intensity function of an inhomogeneous Poisson process is considered when the observable data consists of sampled shot noise that results from passing the Poisson process through an unknown linear time-invariant system. The proposed method consists of first estimating a histogram of the underlying point process. The estimated histogram is used to construct a kernel estimat...