The Equivalence of the Cox Process with Squared Radial Ornstein-Uhlenbeck Intensity and the Death Process in a Simple Population Model

Abstract

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.