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, ARMA processes, estimation and forecasting.
Brzeźniak, Zdzisław; Zastawniak, Tomasz
Basic stochastic processes.
A course through exercises. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., London, 1999.
Norris, James R.
Markov chains.
Reprint of 1997 original. Cambridge Series in Statistical and Probabilistic Mathematics, 2. Cambridge University Press, Cambridge, 1998.
