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.
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.
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
UMU-58020
Application
The online application opens 17 March 2025 at 09:00 CET.
Application deadline is
15 April 2025. 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.
