The correlation parameter of renewal processes and structures with positive and negative periodicity

Abstract

The correlation parameter (CP) as a generalization of the concepts of correlation time and correlation length is calculated for the renewal point structure by studying the spectral density. This structure is a generalization of the renewal process and is characterized by the probability distribution of distances between neighboring points. These distances can be negative. A non-monotonic dependence of the CP on the periodicity parameter is obtained. The results of calculating CPs using spectral densities for various renewal structures are in good agreement with the results of the general formula for quasi-symmetric distributions.