A Martingale Approach to Point Processes in the Plane

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Issue Date
1988-02-05Author
Merzbach, Ely
Nualart, David
Publisher
Institute of Mathematical Statistics (IMS)
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
A rigorous definition of two-parameter point processes is given as a distribution of a denumerable number of random points in the plane. A characterization with stopping lines and relation with predictability are obtained. Using the one-parameter multivariate point-process representation, a general representation theorem for a wide class of martingales is presented, which extends the representation theorem with respect to a Poisson process.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176991900.
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Citation
Merzbach, Ely; Nualart, David. A Martingale Approach to Point Processes in the Plane. Ann. Probab. 16 (1988), no. 1, 265--274. http://dx.doi.org/10.1214/aop/1176991900.
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