CONTINUOUS-STATE BRANCHING PROCESSES
Zenghu Li
These notes were used
in a short graduate course on branching processes the author gave in Beijing
Normal University. The following main topics are covered: scaling limits of Galton--Watson
processes, continuous-state branching processes, extinction probabilities,
conditional limit theorems, decompositions of sample paths, martingale
problems, stochastic equations, Lamperti's transformations, independent and
dependent immigration processes. Some of the results are simplified versions of
those in the author's book “Measure-valued branching Markov processes”
(Springer, 2011). We hope these simplified results will set out the main ideas
in an easy way and lead the reader to a quick access of the subject.
Download the pdf file of the notes.