Bernoulli

  • Bernoulli
  • Volume 5, Number 5 (1999), 797-831.

Point stationarity in d dimensions and Palm theory

Hermann Thorisson

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Abstract

The paper extends to d > 1 dimensions the concept of point-stationarity, which formalizes the intuitive idea of a point process for which the behaviour relative to a given point of the process is independent of the point selected as origin. After defining point-stationarity, this concept is characterized in several ways and the characterizations then used to extend to d dimensions a particular approach to Palm theory, producing two dualities between stationary and point-stationary processes with quite different interpretations. The dualities coincide in the ergodic case.

Article information

Source
Bernoulli, Volume 5, Number 5 (1999), 797-831.

Dates
First available in Project Euclid: 12 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171290400

Mathematical Reviews number (MathSciNet)
MR1715440

Zentralblatt MATH identifier
0953.60029

Keywords
coupling Palm theory point process random field stationarity stochastic geometry

Citation

Thorisson, Hermann. Point stationarity in d dimensions and Palm theory. Bernoulli 5 (1999), no. 5, 797--831. https://projecteuclid.org/euclid.bj/1171290400


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