Main Field of Study and progress level:
Mathematics: Second cycle, has only first-cycle course/s as entry requirements
Grading scale: Three-grade scale
Responsible department: Department of Mathematics and Mathematical Statistics
Established by: Faculty Board of Science and Technology, 2016-06-23
Revised by: Faculty Board of Science and Technology, 2017-10-02
Contents
This course is designed to give an accessible introduction to the numerical discretisation of stochastic differential equations (SDEs). The topics covered are random variables and Wiener processes, examples of SDEs, numerical methods for SDEs and convergence, numerical stability analysis and stochastic geometric numerical integration. Some open research problems are mentioned and applications in finance are discussed.
Expected learning outcomes
For a passing grade, the student must be able to
Knowledge and understanding
clearly describe basic notions of stochastic processes, stochastic differential equations (SDEs) and the concept of convergence of numerical methods applied to SDEs
clearly describe the notion of ergodic limits
Skills
formulate, apply and implement numerical methods for SDEs, including mean-square error estimation and weak error estimates
formulate, apply and implement Monte-Carlo techniques and variance reduction for SDEs
Judgement and approach
select an appropriate numerical method for specific SDEs
numerically evaluate the efficiency of classical schemes for SDEs from molecular dynamics or finance
Required Knowledge
The course requires 30 ECTS in calculus including multivariable calculus and ordinary differential equations, 7.5 ECTS in numerical methods and 6 ECTS in mathematical statistics, or equivalent. 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.
Form of instruction
Teaching is mainly in the form of lectures and supervision of computer labs.
Examination modes
The course is examined by a home assignment with a written report. For the whole course, one of the following grades is assigned: Fail (U), Pass (G), Pass with distinction (VG). A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade. A student who has not received a passing grade after participating in two tests has the right to be assigned another examiner, unless there are certain circumstances prohibiting this (see the Higher Education Ordinance, chapter 6, 22§). A request to be assigned another examiner should be addressed to the head of department for the department of mathematics and mathematical statistics. The possibility of being examined based on the current version of the syllabus is guaranteed for two years following the student's first participation in the course.
Credit transfer All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications.
Other regulations
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
Literature
The literature list is not available through the web.
Please contact the faculty.
