A point process is a probabilistic model for random scatterings of points
on some space often assumed to be a subset of
for some . Oftentimes, point processes describe the occurrence over
time of random events in which the occurrences
are revealed one-by-one as time evolves; in this case, any collection
of occurrences is said to be a realization of the point process.
Poisson processes are regarded as archetypal examples
of point processes (Daley and Vere-Jones 2002).
Point processes are sometimes known as counting processes or random scatters.
often assumed to be a subset of
for some 
. Oftentimes, point processes describe the occurrence over
time of random events in which the occurrences
are revealed one-by-one as time evolves; in this case, any collection
