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    Markov Properties for Point Processes on the Plane

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    NualartD_AP_18(1)342.pdf (1.510Mb)
    Issue Date
    1990-02-02
    Author
    Nualart, David
    Merzbach, Ely
    Publisher
    Institute of Mathematical Statistics (IMS)
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    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.
    URI
    http://hdl.handle.net/1808/17061
    DOI
    https://doi.org/10.1214/aop/1176990952
    Collections
    • Mathematics Scholarly Works [282]
    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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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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