Coalescence in Bellman-Harris and multi-type branching processes
For branching processes, there are many well-known limit theorems
regarding the evolution of the population in the future time. In
this dissertation, we investigate the other direction of the
evolution, that is, the past of the processes. We pick some
individuals at random by simple random sampling without replacement
and trace their lines of descent backward in time until they meet.
We study the coalescence problem of the discrete-time multi-type
Galton-Watson branching process and both the continuous-time
single-type and multi-type Bellman-Harris branching processes
including the generation number, the death time (in the
and the type (in the multi-type processes) of the last common ancestor
( also called the most recent common ancestor) of the randomly
chosen individuals for the different cases (supercritical, critical, subcritical and explosive).