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Stationary stochastic Processes

  • Number of credits 7.5 credits
  • Level Master’s level
  • Starting Autumn Term 2024

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.

Application and eligibility

Stationary stochastic Processes, 7.5 credits

Det finns inga tidigare terminer för kursen Autumn Term 2024 Det finns inga senare terminer för kursen


1 November 2024


19 January 2025

Study location




Type of studies

Daytime, 50%

Required Knowledge

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.

Entry requirements


Guaranteed place Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

Application code



The online application opens 15 March 2024 at 13:00 CET. Application deadline is 15 April 2024. How to apply

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 17,850

Total fee

SEK 17,850

Contact us

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Contactperson for the course is:
Study counselor Lars-Daniel Öhman