| TAMS32 |
Stochastic Processes, 6 ECTS credits.
/Stokastiska processer/
For:
D
I
Ii
IT
MMAT
Y
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
In broad terms, the course treats statistical
models and methods for randomly varying quantities which are
also functions of time. These are fundamental for the advanced
study of telecommunications theory, signal theory, control theory,
robotics, and many important phenomena in biology, physics, computer
networks, and economy. After a completed course the student is expected to be able to:
- describe the basic concepts and theorems in the theory of
stochastic processes, e.g., expectation and autocovariance function and spectral density.
- describe important classes of stochastic processes, e.g.,
the Wiener process, martingales, wide sense stationary processes, and
Markov chains, and their special properties.
- make use of stochastic processes to construct relevant
models for randomly varying quantities which are functions of time.
- carry out important computations for stochastic processes,
such as linear time invariant filtration, and prediction of the values of a process at unobserved times.
- understand and assess models based on stochastic processes and
analyses of such models occurring in other undergraduate courses, or the media.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic courses in probability and statistics. Linear algebra and multivariate analysis. Transform theory is helpful, but not required.
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:
Probability theory, advanced course. Stochastic processes applied to finance. Control theory. Biomedical signal processing. Classification and decision support.
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Organisation:
Lectures and tutorials. Home assignments which are not mandatory but give bonus points at the written examination.
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Course contents:
Multivariate distributions, in
particular the multivariate normal distribution. Conditioning and
conditional expectation. The moment generating function. Stochastic
processes: basic properties and examples. Expectation function,
autocovariance function, cross covariance function. The Poisson
process and the Wiener process. Martingales in discrete time.
Stationary and wide sense stationary processes. Gaussian processes. Mean square
convergence and the mean square integral. Linear time invariant filtering.
Spectral densities. ARMA processes. Prediction. Markov chains in
discrete and continuous time.
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Course literature:
Roy D. Yates & David J.Goodman: Probability and stochastic processes. A Friendly introduction for electrical and computer engineers, 2nd ed. John Wiley, 2005.
Completing material published by the department.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Torkel Erhardsson
Link to the course homepage at the department
Course Syllabus in Swedish
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