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| TAMS45 | Stationary Stochastic Processes, 3 p (sw) /Stationära stokastiska processer/ Advancement level: C | |
| Aim: The course treats theory and methods to handle sequences of observations and continuous registrations where the observations are related. Examples are random models of electronic signals, noise, turbulence, registrations in industrial processes and economical time series. The course is intended as a basis for understanding professional literature in teletransmission theory, control theory, information theory, optimization, queuing networks etc.Prerequisites: Basic courses in mathematical statistics. Theory of analytic functions. Also transform theory is very helpful.Supplementary courses: TAMS50 Applied probability models TSRT35 Control theory TSIT64 Signal theory TBMT11 Biomedical signal processingCourse content: Multivariate distributions, especially the multivariate normal Conditioning. Conditional expectation. Stochastic processes: examples and applications. Poisson process, Brownian Motion (Wiener process). Mean functions and autocorrelation functions. ARMA - processes. Sums of random variables. Moment generating function. Chernoff's inequality. Convergence and criteria of convergence. Martingales. Estimation of a random variable. Mean square criterion, maximum likelihood and maximum a posterior criteria. Properties of estimators. Realization of stationary processes by linear time-invariant systems and spectral methods. Prediction and filtering. Crosscorrelation. Gaussian processes. White Gaussian noise. Renewal processes. Finite Markov chains and stationary distributions. Course literature: Roy D. Yates & David J.Goodman: Probability and random processes. A Friendly introduction for electrical and computer engineers. John Wiley and sons inc 1999. http://www.winlab.rutgers.edu/probability Completing material published by the department. | ||
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