After successful completion of the course, students are able to

• manipulate Brownian motions,
• compute (simple) Ito integrals,
• compute entrance time, entrance probabilities and other properties of Markov chains,
• check the stationarity of stochastic processes,
• compute autocovariance function and other properties of stationary processes,
• estimate AR processes,
• compute linear forecasts.,
• ...

This course provides some further insights into the concepts and methods presented in the lecture. This problem solving course will include theoretical examples as well as applications to simulated and real world data sets.

Exercise sessions.

The course is planned entirely in presence. Changes are possible due to the current COVID situation.

The completed problems have to be marked in TUWEL. Grade distribution:

• more than 80% "sehr gut"
• 71-80% "gut"
• 61-70% "befriedigend"
• 51-60% "genügend"
• less than 51% "nicht genügend".

Brzezniak, Zdzislaw; Zastawniak, Tomasz Basic stochastic processes. A course through exercises. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., London, 1999.

Norris, J. R. Markov chains. Reprint of 1997 original. Cambridge Series in Statistical and Probabilistic Mathematics, 2. Cambridge University Press, Cambridge, 1998.

Deistler, Manfred; Scherrer, Wolfgang. Modelle der Zeitreihenanalyse. Mathematik Kompakt,  Birkhäuser, 2018.

Basic knowledge of probability theory, random variables, expectation, variance, covariance, ...