Signal processing models for point processes

A signal-processing model for the generation of point processes is derived. In the context of this model, the interval between successive events is treated as a time series. The input-output relationship of a system generating inter-event intervals is shown to be derivable from the intensity of the desired point process. Both stationary and non-stationary processes can be generated with this technique. The input-output characteristic of this system is shown to be nonlinear for most interesting cases.