Point Process
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
![<span style=]() {tau_1,tau_2,...,tau_d},tau_1<tau_2<...<tau_d " src="https://mathworld.wolfram.com/images/equations/PointProcess/NumberedEquation1.gif" style="height:15px; width:195px" /> |
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.
REFERENCES:
Brillinger, D. R.; Guttorp, P. M.; and Schoenberg, F. P. "Point Processes, Temporal." Encyclopedia of Environments 3, 1577-1581, 2002.
Daley, D. J. and Vere-Jones, D. An Introduction to the Theory of Point Processes Volume I: Elementary Theory and Methods, 2nd ed. New York: Springer, 2003.
Daley, D. J. and Vere-Jones, D. An Introduction to the Theory of Point Processes Volume II: General Theory and Structure, 2nd ed. New York: Springer, 2007.
Jacobsen, M. Point Process Theory and Applications: Marked Point and Piecewise Deterministic Process. Boston: Birkhäuser, 2006.
