Stationary stochastic Processes 7.5 credits

About the course

The aim of this course is that the student shall acquire 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.

The course covers models for stochastic dependence, concepts for description of stationary stochastic processes in the time domain such as expectation, covariance, and cross-covariance functions, and concepts of description of stationary stochastic processes in the frequency domain such as effect spectrum and cross spectrum. Some important types of processes are introduced: Gaussian processes, Wiener processes, white noise and Gaussian fields in time and space. The course also covers stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), and differentiation and integration of stochastic processes. Finally, the basics in statistical signal processing are introduced, including estimation of expectations, covariance function, spectrum, and applications of linear filters: frequency analysis and optimal filters.

The course consists of two modules:
Module 1 (6 ECTS) Theory and
Module 2 (1.5 ECTS) Computer labs.

Show syllabus

Apply

Autumn 2026
- Stationary stochastic Processes
  
  Second admissions round for EU/EEA citizens
  
  HT26 / Umeå / English / On site
  
  Application opens 16 March 2026
  
  Save education at universityadmissions.se
  
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  Starts
  2 November 2026
  
  Ends
  17 January 2027
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-5800J
  
  Eligibility
  
  The course requires a total of 90 ECTS including a course in Probability Theory on advanced level minimum 7,5 ECTS. Proficiency in English equivalent to the level required for basic eligibility for higher studies.
  
  Selection
  
  Guaranteed place
  
  Application
  The online application opens 16 March 2026 at 09:00 CET. Application deadline is 15 April 2026. Please note: This second application round is intended only for EU/EEA/Swiss citizens.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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