Markov Properties for Point Processes on the Plane

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Issue Date
1990-02-02Author
Nualart, David
Merzbach, Ely
Publisher
Institute of Mathematical Statistics (IMS)
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
It is proved that for a wide class of point processes indexed by the positive quadrant of the plane, and for a class of compact sets in this quadrant, the germ σ-field is equal to the σ-field generated by the values of the process on the set. Therefore, there exists a large family of point processes in the plane (and among them the spatial Poisson process) which satisfy the sharp Markov property in the sense of P. Levy. The strong Markov property with respect to stopping lines is also studied. Some examples are obtained by taking transformations of the probability measure.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176990952.
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Citation
Merzbach, Ely; Nualart, David. Markov Properties for Point Processes on the Plane. Ann. Probab. 18 (1990), no. 1, 342--358. http://dx.doi.org/10.1214/aop/1176990952.
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