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.
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.
M. Deistler and W. Scherrer. Time Series Models. Springer, 2022.
Basic knowledge of probability theory, random variables, expectation, variance, covariance, ...