A non-renewal process with renewal counting distributions

Marcel F. Neuts
1987 Advances in Applied Probability  
A simple example is given of a point process with dependent inter-event intervals for which the distributions of the counting random variables Nt are given by the same formulas as for a renewal process. This example shows the care needed in establishing that a given point process has the renewal property, but also raises interesting questions about the class of point processes with given counting distributions.
doi:10.2307/1427384 fatcat:7hxme4dlgzde5i7g2kituyfqlm