@article{EJP390,
author = {B.Gail Ivanoff and Ely Merzbach and Mathieu Plante},
title = {A Compensator Characterization of Point Processes on TopologicalLattices},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {point process, compensator, partial order, single jump process, partial sum process,adapted random set, renewal process,Poisson process, multiparameter martingale},
abstract = {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},
pages = {no. 2, 47-74},
issn = {1083-6489},
doi = {10.1214/EJP.v12-390},
url = {http://ejp.ejpecp.org/article/view/390}}