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Point Process


A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. 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

 {tau_1,tau_2,...,tau_d},tau_1<tau_2<...<tau_d

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.


See also

Marked Point Process, Poisson Process, Self-Correcting Point Process, Self-Exciting Point Process, Simple Point Process, Spatial Point Process, Spatial-Temporal Point Process, Temporal Point Process

This entry contributed by Christopher Stover

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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.

Cite this as:

Stover, Christopher. "Point Process." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PointProcess.html

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