Poisson Birth Process

The model assumes births follow a Poisson point process with time-dependent intensity. The two-dimensional marked Poisson representation models each person by birth time and lifespan. Birth intensity is modeled exponentially for entry ages 0, 30, and 60. The Poisson construction explains why transition probabilities for the oldest-person process can be computed. Increasing population size through the birth process contributes to an increasing expected age for the oldest living person.