The Poisson point process is a type of random object in mathematics known as a point
process. For over a century this point process has been the focus of much study and …

In 1972, the proceedings of a confer-ence on stochastic point processes, organized by Peter
Lewis the previous year, were published (Lewis (1972)); the volumeis unfortunately out of …

The archetypal point processes are the Poisson and renewal processes. Their importance is
so great, not only historically but also in illustrating and motivating more general results, that …

In this paper we discuss the complementary theorem applied to the typical n-tuple of a
Poisson point process. The theorem was first presented by Miles in 1970 and discussed by …

We discuss strong Markov property of Poisson point processes and the related stopping
sets. Viewing Poisson process as a set indexed random field, we demonstrate how the …

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter
point process into a planar Poisson process of unit rate, using random stopping sets …

Point processes serve as probabilistic models for random locally finite point patterns on
some general space. Their distributions are typically rather involved objects, and it is …

This paper introduces a new graph constructed from a point process. The idea is to connect
a point with its nearest neighbour, then to the second nearest and continue this process until …

Point processes are mathematical models for irregular or random point patterns. A short
introduction to the theory of point processes and their statistics, emphasizing connections …

The Poisson process, a core object in modern probability, enjoys a richer theory than is
sometimes appreciated. This volume develops the theory in the setting of a general abstract …