| TAMS47 | Stochastic Processes, 4,5 ECTS credits. /Stokastiska processer/ |
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Prel. scheduled
hours: 50 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(A-D): C
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| 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. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Basic courses in mathematical statistics. Theory of analytic functions. Also transform theory is very helpful. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Supplementary courses: TAMS46 Probability, second course TSRT35 Control theory TBMT01 Biomedical signal processing TBMI27 Classification and decision support |
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| Organisation: |
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| Course contents: 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, Kalman filters. Mean square criterion, maximum likelihood and maximum a posterior criteria. Realization of stationary processes by linear time-invariant systems and spectral methods. Prediction and filtering. Crosscorrelation. Gaussian processes. White Gaussian noise. Finite Markov chains and stationary distributions. |
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| Course literature: Roy D. Yates & David J.Goodman: Probability and random processes. A Friendly introduction for electrical and computer engineers, Second Edition. John Wiley and sons inc 2005. http://www.winlab.rutgers.edu/probability Completing material published by the department. |
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| Examination: | |||
| Written examination |
3 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Eva Enqvist Examiner: Timo Koski, tikos@mai.liu.se Link to the course homepage at the department Course Syllabus in Swedish |
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