Statistical properties of several models of fractional random point processes

Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.

Research highlights
► Application of the fractional processes theory to statistical optics.
► Nonclassical properties of fractional point processes.
► Simulation of fractional point processes.