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.

Brownian motion (Wiener process); Definition and properties; construction of the stochastic integral and properties; Ito isometry and Ito formula; Markov chains in discrete time; definition and fundamental formulas; application of the Markov property; classification of states; introduction to time series analysis: stationary processes (in discrete time), auto covariance function, AR processes, ARMA processes, estimation and forecasting.

Mixed presentations with slides and on blackboard

The performance is assessed by an examination at the end of the semester.
See: https://fam.tuwien.ac.at/lehre/pr/

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, ...