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Stochastic Differential Equations

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

About the course

This course covers a generalization of the classical differential- and integral calculus using Brownian motion. With this, Ito calculus stochastic differential equations can be formulated and solved, numerically and in some cases analytically. This yields a powerful tool for describing and simulating random phenomena in science, engineering and economics. The course starts with a necessary background  in probability theory and Brownian motion. Then the Ito integral and the fundamental theorem of Ito calculus, Ito’s lemma, are introduced. Furthermore, numerical and analytical methods  for the solution of stochastic differential equations are considered. The connections between stochastic differential equations and partial differential equations are investigated (the Feynman-Kac formula, the Fokker-Planck equation). Some applications of stochastic differential equations are presented. Mandatory computer assignments are included.

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.

Application and eligibility

Stochastic Differential Equations, 7.5 credits

Visa tillfällen för föregående termin 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 90 ECTS including 22,5 ECTS in Calculus of which 7,5 ECTC in Multivariable Calculus and Differential Equations, a basic course in Linear Algebra minimum 7,5 ECTS and a basic course in Mathematical Statistics minimum 6 ECTS. Proficiency in English and Swedish 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