Course detail
Stochastic Processes
FIT-SSPAcad. year: 2014/2015
The course provides the introduction to the theory of stochastic processes. The following topics are dealt with: Types and basic characteristics, covariation function, spectral density, stationarity, examples of typical processes, time series and evaluating, parametric and nonparametric methods, identification of periodical components, ARMA processes. Applications of methods for elaboration of project time series evaluation and prediction supported by the computational system MATLAB.
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Course curriculum
- Syllabus of lectures:
- Stochastic processes, trajectories, examples, classification of stochastic processes.
- Consistent system of distribution functions, strict and weak stationarity.
- Momentum characteristics: the mean value, autocorrelation and partial autocorrelation, spectral density.
- Poisson processes.
- Statistical analysis of Poisson processes.
- Markov processes.
- Birth and death processes.
- Markov strings, transition probabilities, properties.
- Homogeneous Markov strings, state classification and stationary probabilities.
- Time series, stationarity, ergodicity.
- Trend estimation and methods of prediction.
- AR and MA processes.
- ARMA processes.
- Statistical software Statistica, Statgraphics, Matlab.
- Reading and visualizing data. Simulation.
- Descriptional statistics of time series.
- Momentum characteristics of stochastic processes.
- Selected properties of Poisson processes: practical usage.
- Real-life examples of Poisson processes, applications in the theory of reliability, defect analyzis.
- Markov processes: examples, models of queues, looking for limit state probabilities.
- Yule's birth processes: computing state probabilities, examples of applications on processes of growth and death.
- Markov strings: practical examples, construction of matrices of transition probabilities, computation of state probabilities for homogeneous strings.
- Practical examples of state classification, computation of stationary probabilities.
- Analysis of time series, trend estimation.
- Computing autocorrelation and partial autocorrelation functions, AR(1) and MA(1) processes.
- Model identification, computing predictions using up-to-date software.
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Classification of course in study plans
- Programme IT-MSC-2 Master's
branch MBI , 0 year of study, winter semester, elective
branch MBS , 0 year of study, winter semester, elective
branch MMI , 0 year of study, winter semester, elective
branch MMM , 0 year of study, winter semester, compulsory-optional
branch MPV , 0 year of study, winter semester, elective
branch MSK , 0 year of study, winter semester, elective