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Self-Exciting Point Process

A self-exciting point process, in the covariance formulation, is a temporal point process N such that

cov(N(s,t),N(t,u))>0

for s<t<u in its time domain, assuming these covariances exist. Here, N(s,t) denotes the number of points in the interval (s,t], and cov denotes covariance (Schoenberg 2011). Intuitively, the occurrence of past points makes the occurrence of future points more probable.

See also

Marked Point Process, Point Process, Self-Correcting 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

Schoenberg, F. P. "Introduction to Point Processes." In Wiley Encyclopedia of Operations Research and Management Science. New York: Wiley, 2011. https://doi.org/10.1002/9780470400531.eorms0425.

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Self-Exciting Point Process

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Self-Exciting Point Process." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Self-ExcitingPointProcess.html

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