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2007 A Compensator Characterization of Point Processes on Topological Lattices
B.Gail Ivanoff, Ely Merzbach, Mathieu Plante
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Electron. J. Probab. 12: 47-74 (2007). DOI: 10.1214/EJP.v12-390


We resolve the longstanding question of how to define the compensator of a point process on a general partially ordered set in such a way that the compensator exists, is unique, and characterizes the law of the process. We define a family of one-parameter compensators and prove that this family is unique in some sense and characterizes the finite dimensional distributions of a totally ordered point process. This result can then be applied to a general point process since we prove that such a process can be embedded into a totally ordered point process on a larger space. We present some examples, including the partial sum multiparameter process, single line point processes, multiparameter renewal processes, and obtain a new characterization of the two-parameter Poisson process


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B.Gail Ivanoff. Ely Merzbach. Mathieu Plante. "A Compensator Characterization of Point Processes on Topological Lattices." Electron. J. Probab. 12 47 - 74, 2007.


Accepted: 14 January 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60085
MathSciNet: MR2280258
Digital Object Identifier: 10.1214/EJP.v12-390

Primary: 60K05
Secondary: 60G48 , 60G55

Keywords: adapted random set , compensator , multiparameter martingale , partial order , partial sum process , point process , Poisson process , Renewal process , single jump process

Vol.12 • 2007
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