Point-stationarity in \(d\) dimensions and Palm theory
type: Item
instance of: scholarly article
title: Point-stationarity in \(d\) dimensions and Palm theory
zbMATH Open document ID: 0953.60029
DOI: 10.2307/3318445
author: Hermann Thorisson
published in: Bernoulli
publication date: 2001-01-22T00:00:00Z
review text: The author extends to \(d>1\) dimensions the concept of point-stationarity, which formalizes the intuitive idea of a simple point process for which the behavior relative to a given point of the process is independent of the point selected as origin. Note that point-stationarity is different from stationarity. For \(d=1\), the Poisson process with constant intensity is stationary since if the origin is moved from 0 to any other fixed site \(t\), then we still have a Poisson process with the same intensity. But if a point is added at 0, then we obtain a non-stationary process since if the origin is moved from the point which we placed at 0 to any other fixed site \(t\), then there need not be a point there. This new process is point-stationary since, seen from the point which we placed at 0, the intervals between points are i.i.d. exponential. After defining point-stationarity, this concept is characterized in several ways and the characterizations then are used to extend to \(d\) dimensions a particular approach to Palm theory.
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1396205
zbMATH Keywords: Palm theory
zbMATH Keywords: coupling
zbMATH Keywords: stationarity
reviewed by: Viktor Ohanyan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/3318445
OpenAlex ID: W2006250597
description: scientific article; zbMATH DE number 1396205