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Temporal Point Process


A temporal point process is a point process whose realizations consist of the times {tau_j}_(j in J) of isolated events.

The event times tau_j are real numbers; depending on the observation interval and realization, the index set J may be finite or countable. Binary indicators can record whether an event occurs in each small time bin, but these indicators are not the event times themselves (Brillinger et al. 2002, Eden 2013).

The behavior of a simple temporal point process N is typically modeled by specifying its conditional intensity lambda=lambda(t). For example, Poisson processes and Hawkes processes are modeled using specified conditional intensity functions (Schoenberg 2011).


See also

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

Portions of 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 Environmetrics 3, 1577-1581, 2002.Eden, U. "Chapter 2: Introduction to Point Processes." 2013. https://sites.stat.columbia.edu/liam/teaching/neurostat-fall13/uri-eden-point-process-notes.pdf.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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Temporal Point Process

Cite this as:

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

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