Stohastic Processes

Subject description

1. Stochastic processes.

– What is a stochastic process?

– How to describe a stochastic process?


2. Markov chains.

– Discrete time Markov chains.

– Classification of states.

– Strong Markov property.

– Stationary distributions.

– Ergodic properties of Markov chains.

– Monte Carlo simulation.

– Continuous time Markov chains.

– Continuous time Markov chains: examples of application.


3. Time series.

– Examples of time series.

– Stationary time series.

– Autocorrelation and partial autocorrelation.

– ARIMA models.

– Parameter estimation in ARIMA models.

– Kalman filter.

The subject is taught in programs

Objectives and competences

Students get acquainted with stochastic processes in discrete and continuous time as well as some of the applications. Objectives include elements of time series.

Teaching and learning methods

Lectures, exercises, homeworks, projects, study of literature, consultations.

Expected study results

Knowledge and understanding:

Of time dependence of stochastic phenomena both with respect to discrete time (including time series) and continuous time. This includes some applications of the theory.

Basic sources and literature

  • G. R. Grimmett in D. R. Stirzaker, Probability and Random Processes, 2nd Ed., Oxford Science Publications, 1997.

  • R. L. Tweedie, Markov chains and stochastic stability, Springer, 1996.

  • P. J. Brockwell, R. A. Davis, Time series: theory and methods, Springer, 1991.

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