The Correlation Function of Multiple Dependent Poisson Processes Generated by the Alternating Renewal Process Method

TL;DR

This paper develops a method using alternating renewal processes to generate correlated Poisson processes, deriving conditions and correlation functions, including negative correlations, with potential extensions to multiple dependent renewal processes.

Contribution

It introduces a novel approach to construct correlated Poisson processes using alternating renewal processes, providing conditions and correlation analysis.

Findings

Derived conditions for using alternating renewal processes to generate correlated Poisson processes.

Obtained the pairwise correlation function, showing possible negative correlations.

Method can be extended to multiple dependent renewal processes.

Abstract

We derive conditions under which alternating renewal processes can be used to construct correlated Poisson processes. The pairwise correlation function is also derived, showing that the resulting correlations can be negative. The technique and the analysis can be extended to the generation of two or more dependent renewal processes.