Population-size-dependent and age-dependent branching processes

Critical Age Dependent Branching Markov Processes and Their Scaling Limits

This paper studies: (i) the long time behaviour of the empirical distribution of age and normalised position of an age dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age dependent critical branching Brownian motions.

Calculations for multi-type age-dependent binary branching processes.

This article provides a method for calculating the joint probability density for the topology and the node times of a tree which has been produced by an multi-type age-dependent binary branching process and then sampled at a given time. These processes are a generalization, in two ways, of the constant rate birth-death process. There are a finite number of types of particle instead of a single ...

A Path Integral Approach to Age Dependent Branching Processes

We develop a fully stochastic theory for age-structured populations via quantum field theoretical methods. The operator formalism of Doi is first developed, whereby birth and death events are represented by creation and annihilation operators, and the complete probabilistic representation of the age-chart of a population is represented by states in a suitable Hilbert space. We then use this for...

On the Theory of Age-Dependent Stochastic Branching Processes.

Multi-type branching processes with time-dependent branching rates

Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as t...