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A Martingale Approach to Point Processes in the Plane

Merzbach, Ely
; 
Nualart, David
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Abstract
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.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176991900.
Date
1988-02-05
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Publisher
Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_AP_16(1)265.pdf
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Keywords
Two-parameter point process, stopping line, martingale representation, multivariate point process, Poisson process, predictable projection
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.
URI
https://hdl.handle.net/1808/17064
DOI
10.1214/aop/1176991900
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