Simple point process

A simple point process is a special type of point process in probability theory. In simple point processes, every point is assigned the weight one.

Definition

Let be a Locally [compact space|locally compact] second countable Hausdorff space and let be its Borel -algebra. A point process, interpreted as random measure on, is called a simple point process if it can be written as
for an index set and random elements which are almost everywhere pairwise distinct. Here denotes the Dirac measure on the point.

Examples

Simple point processes include many important classes of point processes such as Poisson processes, Cox processes and binomial processes.

Uniqueness

If is a generating ring of then a simple point process is uniquely determined by its values on the sets. This means that two simple point processes and have the same distributions iff

Literature

Category:Point processes