Abstract
This 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.
| Original language | English |
|---|---|
| Pages (from-to) | 797-831 |
| Number of pages | 35 |
| Journal | Bernoulli |
| Volume | 5 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1999 |
Other keywords
- Coupling
- Palm theory
- Point process
- Random field
- Stationarity
- Stochastic geometry