Modeling and analyzing fractal point processes

Abstract

Fractal point processes are modeled as doubly stochastic point processes for which the intensity is a fractal stochastic waveform process. With this model, the fractal point process is shown to be self-similar only over long time scales, with short time scales exhibiting little fractal effects. Parameters of the fractal process are measured with the Fano factor: the ratio of the variance to the mean of the number of events occurring in a time interval. The application of the analysis techniques is illustrated by an example taken from single auditory neuron recordings. >