After successful completion of the course, students are able to understand the basic concepts underlying the theory of discrete-time and continuous-time Markov chains and discrete-time martingales. They are also able to apply these concepts in a variety of applications.

See lectures

Discussion of the problem sheets previously provided by the lecturer

In principle, this UE course should run for 2 hours per week, from the beginning of March to the beginning of May. In any case, the schedule is provisional and will be discussed with the students in the first week (for example, we may change date/time or run it for fewer weekly hours over a longer period, e.g. until the end of May). If the provisional schedule does not work for you, please drop an email to the lecturer before the start of the semester and indicate your preference.

Students will be required to work out problems at home and present them during the class. They will be evaluated based on how many problems they managed to solve and, more importantly, on the quality of their presentations.

• Norris, J. (1997). Markov Chains. Cambridge University Press. doi:10.1017/CBO9780511810633
• Williams, D. (1991). Probability with Martingales. Cambridge University Press. doi:10.1017/CBO9780511813658

Basic probability theory, calculus and linear algebra