Stochastic Processes, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Mathematics, Master's Programme
• Computer Science and Engineering, M Sc in Engineering
• Industrial Engineering and Management - International, M Sc in Engineering
• Industrial Engineering and Management, M Sc in Engineering
• Information Technology, M Sc in Engineering
• Applied Physics and Electrical Engineering - International, M Sc in Engineering
• Applied Physics and Electrical Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Intended learning outcomes

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.

Course content

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.

Teaching and working methods

Lectures and tutorials. Home assignments which are not mandatory but give bonus points at the written examination.

Examination

Grades

Other information

Supplementary courses: Probability theory, advanced course. Stochastic processes applied to finance. Control theory. Biomedical signal processing. Classification and decision support.

Department

Director of Studies or equivalent

Examiner

Course website and other links

Education components

Course literature

Additional literature

Books

• Roy D. Yates & David J.Goodman, (2005) Probability and stochastic processes. A Friendly introduction for electrical and computer engineers 2nd ed John Wiley

Other