Specialization "Stochastics and Dynamical Systems" (SDS)

This page collects the most important information about the specialization "Stochastics and Dynamical Systems", for Master's und doctoral programs.

Master's program

In the Master's program, "Stochastics and Dynamical Systems" is one of 7 main areas of specialization. If this is the chosen main area of specialization, there is a compulsory module group of foundational courses. (The further modules of the Master's program can be divided between courses from the chosen area of specialization and courses from other areas of specialization.)

The standard curriculum in this area of specialization consists of 4 compulsory modules:

• The module on stochastic processes introduces the most important types of random processes, in particular Markov chains in discrete and continuous time (like random walks and branching processes), and some of their applications. This course should be taken at the very start of the Master's program.
• The module on measure theory and integration provides the analytical basis for most of the other courses here. It should also be taken at the very start of the Master's program.
• The module on advanced probability theory covers the core material of probability in a measure-theoretic framework. Its topics include the law of large numbers, distributional convergence, central limit theorems, existence of stochastic processes, Brownian motion, and invariance principles.
• Seminars on SDS.

Further lecture courses on advanced topics often reflect the research interests of faculty members. We regularly offer courses on stochastic analysis, financial mathematics, ergodic theory, and further aspects of dynamical systems.

It is advisable to think about a possible topic and a supervisor of a master's thesis at an early stage of the Master's program, and to contact potential supervisors in time. There is a broad range of topics suitable for Master's theses.  Theses closely related to current research, however, usually study topics from some faculty member's field or research. Information on those can be found on the webpages.

Doctoral program

As usual at the Faculty of Mathematics, there is no real difference between advanced courses for the Master's program and courses for the doctoral program in the area of specialization "Stochastics and Dynamical Systems". The recognition of courses for the doctoral program will be specified individually in the "dissertation agreement" (Dissertationsvereinbarung). In particular, it is irrelevant for the recognition of a course whether the course  is announced with a course number for the Master's in mathematics (25XXXX) or for the doctoral (51XXXX) program. You can find general information on the doctoral program on the web pages of the SSC Mathematics and the Center of Doctoral Studies of the University of Vienna.

The research interests of the individual faculty members play a much larger role in the choice of a topic and supervisor for a doctoral dissertation than for a Master's thesis: dissertation topics are usually adjacent to the research area and interests of the supervisor, which can be found on their personal homepages.