Topics in Branching Processes
TU Berlin, Summer 2025. Lecturer: Tejas Iyer. 5 ECTS, taught in English.
Materials
Organisation
Lectures were held on Tuesdays 16:00–18:00, from 15 April to 15 July 2025. Assessment was by oral exam.
Description
Branching processes are a natural model for the growth of a population over time, and are important in biology and other areas; perhaps the best-known application is epidemic modelling. The course covers the classical discrete-time Bienaymé–Galton–Watson process and, time permitting, processes with immigration and age-dependent processes:
- Generating functions and classical extinction criteria.
- Asymptotic theory for subcritical, critical and supercritical processes: the Kolmogorov and Yaglom limits, the Kesten–Stigum theorem and Seneta–Heyde norming.
- Continuous-time branching processes and age-dependent processes.
- Computational methods: simulations and modelling applications such as epidemiological spread.
Prerequisites
Officially Probability I and II. Basic knowledge of Markov chains, conditional expectations and martingales (including the martingale convergence theorem) is enough to follow the course.
Learning outcomes
On satisfying the requirements of this course, students will have a deeper understanding of branching processes and their connections to applications and other areas of probability. Students will be well-equipped to:
- Explain fundamental concepts concerning branching processes, and their role in applied contexts.
- Apply branching-process arguments, as well as more fundamental probabilistic techniques such as martingales, in a variety of problem-solving contexts.
Theses
Students may use this course as preparation for a Bachelor’s or Master’s thesis with me. Wolfgang König is also happy to supervise Bachelor’s and Master’s theses on this topic.
Key references
- K. B. Athreya and P. E. Ney, Branching Processes. Dover, 2004.
- R. Lyons and Y. Peres, Probability on Trees and Networks. Cambridge University Press, 2017.