A Compensator Characterization of Point Processes on Topological
Lattices
B.Gail Ivanoff, University of Ottawa
Ely Merzbach, Bar-Ilan University
Mathieu Plante,
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
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