Two kinds of stationary point process are considered. One is generated by the sequence of death times in a simple immigration, birth and death process; the other is the Cox process with intensity given by the square of the radial Ornstein-Uhlenbeck process. By comparison of the coincidence densities, we show that the two classes of processes are equivalent. An explicit expression is given for the coincidence density of arbitrary order.
"The Equivalence of the Cox Process with Squared Radial Ornstein-Uhlenbeck Intensity and the Death Process in a Simple Population Model." Ann. Appl. Probab. 3 (3) 863 - 873, August, 1993. https://doi.org/10.1214/aoap/1177005368