Abstract
In this survey paper, two-parameter point processes are studied in connection with martingale theory and with respect to the partial-order induced by the Cartesian coordinates of the plane. Point processes are characterized by jump stopping times and by their two-parameter compensators. Properties of the doubly stochastic Poisson process, such as predictability, are discussed. A definition for the Palm measure of a two-parameter stationary point process is proposed.
| Original language | English |
|---|---|
| Pages (from-to) | 79-101 |
| Number of pages | 23 |
| Journal | Acta Applicandae Mathematicae |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1988 |
Keywords
- AMS subject classifications (1980): 60G55, 60G40, 60G57, 60G60
- Palm measure
- Point process
- compensator
- doubly stochastic Poisson process
- intensity
- martingale
- optional increasing path
- orderliness
- partial-order
- predictability
- stationarity
- stopping line