A temporal point process is a point process whose realizations consist of the times of isolated events.
The event times
are real numbers; depending on the observation interval and realization, the index
set
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
is typically modeled by specifying its conditional
intensity
.
For example, Poisson processes and Hawkes
processes are modeled using specified conditional
intensity functions (Schoenberg 2011).