The Age-Dependent Process: Markov Case

Abstract

This chapter is devoted to the use of time-continuous branching process with exponential life-time distributions. This process also has the Markov property and is closely related to the Galton–Watson process. The exponential distribution to model lifetimes of particles is not well motivated by any biological assumptions. Indeed, the exponential distribution admits lifetimes which are arbitrarily close to 0, while it is known that life cycles of organisms and cells have lower bounds of durations, which are greater than 0. The advantage of using the exponential distribution is that it leads, in many cases, to computable expressions. These expressions allow one to deduce properties which can then be conjectured for more general models.