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January, 1990 Markov Properties for Point Processes on the Plane
Ely Merzbach, David Nualart
Ann. Probab. 18(1): 342-358 (January, 1990). DOI: 10.1214/aop/1176990952


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 $\sigma$-field is equal to the $\sigma$-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.


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Ely Merzbach. David Nualart. "Markov Properties for Point Processes on the Plane." Ann. Probab. 18 (1) 342 - 358, January, 1990.


Published: January, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0711.60045
MathSciNet: MR1043951
Digital Object Identifier: 10.1214/aop/1176990952

Primary: 60J75
Secondary: 60G55 , 60G60 , 60J25 , 60J30

Keywords: absolutely continuous transformation , germ $\sigma$-field , Markov property , point process , Poisson sheet , stopping line , strong Markov property

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 1 • January, 1990
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