The Annals of Probability

A Martingale Approach to Point Processes in the Plane

Ely Merzbach and David Nualart

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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.

Article information

Source
Ann. Probab., Volume 16, Number 1 (1988), 265-274.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991900

Digital Object Identifier
doi:10.1214/aop/1176991900

Mathematical Reviews number (MathSciNet)
MR920270

Zentralblatt MATH identifier
0639.60055

JSTOR
links.jstor.org

Subjects
Primary: 60G55: Point processes
Secondary: 60G48: Generalizations of martingales 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G60: Random fields

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. doi:10.1214/aop/1176991900. https://projecteuclid.org/euclid.aop/1176991900


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