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Stochastic Differential Equations

  • Number of credits 7.5 Credits
  • Level Master’s level
  • Starting Autumn Term 2018

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 hp

Visa tillfällen för föregående termin Autumn Term 2018 Det finns inga senare terminer för kursen

Starts

Lectures begin on week starting 5 November 2018

Ends

Lectures end during the week of 14 January 2019

Study location

Umeå

Language

English (upon request)

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 equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
 

Selection

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 15 March 2018 at 13:00 CET. Application deadline is 16 April 2018.

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

SEK900

Tuition fee, first instalment

SEK16,875

Total fee

SEK16,875

Contact us

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

Please be aware that the university is a state body and that what you write here can be included in a public document. Therefore, be careful if you are writing about sensitive or personal matters in this contact form. If you have a such an enquiry, please call us instead. All data will be treated in accordance with The Personal Data Act.

Course is given by
Dept of Mathematics and Mathematical Statistics