Lecture:

Tuesdays, 10am - 12pm, room M4
Fridays, 10am - 12pm, room M4

Lecturer: 

Prof. Dr. Gerold Alsmeyer

Assistance: 

tba

QISPOS:

The course in the course catalogue
The tutorial in the course catalogue

Course syllabus:

Branching processes form one of the fundamerntal type of stochastic processes and are typically introduced in order to describe population growth. The most fundamental and classical population model assumes that individuals reproduce independently and have a random number of offspring, the distribution of which is the same for all individuals and called offspring distribution. Starting from one individual, called ancestor, which forms generation 0, the number of individuals in generation n defines a random process, called Galton-Watson branching process. The systematic study of this process including variants thereof is the main topic of this course. Important questions of interest are: (1) Sufficient conditions ensuring almost certain extinction. (2) The growth behavior of the process in the case of non-extinction. These will be addresses in some detail, basic tools being probability generation functions and martingale theory. More advanced questions are concerning the genealogical tree associated with a Galton-Watson branching process, which obvioulsy forms a random tree. Such questions might be addresses in the last part of the course.

Many of the fundamental results 

Learnweb:

The corresponding Learnweb course can be found here. The key is: MMIDB

Course assessment:

There will be an oral exam at the end of the course. Admission to the oral exam is conditional on obtaining at least 40% of the points of the problem sets.

Tutorial:

Wednesdays, 10:00 - 12:00 Uhr, rtba

Problem sets:

The problem sets can be found in the Learnweb course.