Point processes in the plane

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6 Scopus citations


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 languageEnglish
Pages (from-to)79-101
Number of pages23
JournalActa Applicandae Mathematicae
Issue number1
StatePublished - May 1988


  • 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


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