Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Probability Theory and Statistics
- Code
- stacfo1u0um17em
- Title
- Stationary processes (l)
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with the modern notions of stationary processes Ability: to understand and use stationary processes Attitude: the need to extend the mathematical knowledge, to gain new analytic and applied programming skills Autonomy and Responsibility: based on the gained knowledge in stationary processes, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Stationary processes. Covariance function. Bochner–Hinczin theorem. (Herglotz theorem) Karhunen-Loeve series analysis, Kotelnikov-Shannon theorem - sampling density. Completely regular and singular processes. Linear filters. Ergodicity. Estimation of the expected value and covariance function of stationary processes. Estimation of the spectrum. Periodogram. Discrete spectrum, continuous spectrum. Consistent estimation of the spectrum, smoothing, use of window functions. Mixed spectrum processes. State space description of stationary processes with discrete parameters. Ho-Kalman algorithm, Faurre-Anderson theory.
- Assessment method
- exam
- Bibliography
- lecture notes