Course Syllabus for

Stationary Stochastic Processes
Stationära stokastiska processer

FMSF10F, 7.5 credits

Valid from: Autumn 2020
Decided by: Anders Gustafsson / FUN
Date of establishment: 2020-05-18

General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSF10
Teaching language: English


The student shall aquire a toolbox containing concepts and models for description and handling of stationary stochastic processes within many different areas, such as, signal processing, automatic control, information theory, economics, biology, chemistry, and medicine. The mathematical and statistical elements are therefore illustrated using a wide variety of examples from different areas of application. The course shall also give the student the ability to identify the presence of stationary processes in other courses in the education, use the knowledge of stationary processes in other courses, and translate the concepts and tools between different courses, building on stationary processes.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must

Course Contents

Models for stochastic dependence. Concepts of description of stationary stochastic processes in the time domain: expectation, covariance, and cross-covariance functions. Concepts of description of stationary stochastic processes in the frequency domain: power spectrum, cross spectrum. Special processes: Gaussian process, Wiener process, white noise, Gaussian fields in time and space. Stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), derivation and integration of stochastic processes. The basics in statistical signal processing: estimation of expectations, covariance function, and spectrum. Application of linear filters: frequency analysis and optimal filters.

Course Literature

Lindgren, G., Rootzén, H., Sandsten & M.: Introduction to Stationary Stochastic Processes: Applications in Science and Engineering.. Chapman & Hall, 2013. ISBN 9781466586185.

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination format: Written exam
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: A basic course in mathematical statistics and knowledge in complex and linear analysis.

Course Occasion Information

Contact and Other Information

Course coordinator: Maria Sandsten <>
Web page:

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