Lecturer: Tejas Iyer
Lecture notes: Available here
ROOM UPDATE!!!: FROM 10/06/2025 we will be in room MA750.
Class format: Every Tuesday 16-18, starting 15/04/2025 until 15/07/2025. (See also Moses and ISIS)
Contact: After lectures, or email me - [first].[lastname]@wias-berlin.de
Language: English
Assessment: Oral exam
Credits: 5 ECTS
Course description: Branching processes are a natural model for the growth of a population over time, hence are important for various applications, in biology, and other areas. Perhaps the most well-known application comes from epidemic modelling, where one seeks to model the number of the spread of a disease over time.
This course will delve into topics concerning the classical, discrete time Bienyamé-Galton-Watson processes, and then, time-permitted, delve into more general processes with immigration and age-dependent processes. Time permitted, we will cover some of the following topics:
Use of generating functions and classical extinction criteria.
Asymptotic limit theory for subcritical, critical and supercritical Bienyamé-Galton-Watson processes. The Kolmogorov and Yaglom limits, 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.
Branching processes are closely connected to the study of random graphs, hence participants may also be interested in the other lecture course taking place this semester.
Pre-requisites: Officially Probability I and II. However, if you know some basics about Markov chains, conditional expectations and martingales (including the martingale convergence theorem) feel free to attend. Send me an email if you have any doubts.
Learning outcomes: On satisfying the requirements of this course, students will have a deeper understanding of topics concerning 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 other more fundamental probabilistic techniques such as martingales, in a variety of problem solving contexts.
Students may use this course in preparation for a bachelors or masters thesis with me. Wolfgang König is happy to supervise bachelors and masters theses in this topic until 2032.
Resources: Lecture notes will be provided as the course progresses.
Much of the material we intend to cover is included in the texts:
K.B. Athreya and P.E. Ney. Branching Processes. Dover Books on Mathematics. Dover Publications, 2004.
R. Lyons and Y. Peres. Probability on Trees and Networks. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2017.