Interaction between two independent recurrent time series

Abstract

Two mutually independent recurrent processes, each consisting of a time series of events, are considered. The durations of the intervals between the events in each series are independent of each other and identically distributed with a probability density function φ(t) and ψ(t). Every event of the ψ(t) process annihilates the next event of the φ(t) process. The probability density function of the intervals of the thus transformed φ(t) process is derived, and possible fields of application are mentioned. The φ(t) or the ψ(t) process, being Poisson, are treated as special cases.