Postgraduate course on

Numerical Methods for Stochastic Differential Equations

Lecturers: Kevin Burrage (U of Queensland), Erik Johnson (USC), Arvid Naess (NTNU), Tomas Björk (Handelshögskolan) and Anders Szepessy (KTH)

During the spring semester of 2001, the National Network in Applied Mathematics (NTM) will organise a postgraduate course on numerical methods for stochastic differential equations (SDEs). The course is primarily directed towards to PhD students in mathematics, mathematical statistics and numerical analysis. It will be open to PhD students within NTM's graduate school, to PhD students from other research networkds such as NGSSC, to other PhD students from the Nordic and Baltic countries and also to participants from industry and business.

Course schedule

The course will consist of two intensive weeks in Stockholm 2-6 April and in Lund 7-11 May. After each of these weeks a smaller project is to be carried out and documented in a written report. During the intensive weeks lectures will be given in the mornings while assignments and computer exercises will be done in the afternoons.

Course contents

The first week starts with Tomas Björk giving an introduction to SDEs (6 hrs). Thereafter the main theme is simulation of realisations of SDEs and of expectations of functions of solutions to SDEs using Monte Carlo methods. This part is taught by Kevin Burrage and Anders Szepessy.

The theme for the second course week is numerical computation of the distribution of solutions to SDEs using methods like finite elements, finite differences and path integration. This part is taught by Erik Johnson and Arvid Naess.

A detailed plan of the course contents can be found here.

Those who want to take the course for credits must actively work with assignments handed out during the course, take part in the computer exercises and must also do the small projects. The course is suggested to give 5 course credits in a PhD programme.

Literature

We recommend Stochastic Differential Equations by Bernt Oksendahl (Springer-Verlag) as a basic book on SDEs. For those who want a financial perspective, Arbitrage Theory in Continuous Time by Tomas Björk (Oxford University Press) is good reading. Tomas' transparencies are available here.

For Anders Szepessy's part, lecture notes (Chapters 2-7) are available here.

Kevin Burrage will hand out lecture notes from a book draft and slides in Power Point format will be available prior to the course.

For Arvid Naess' part, lecture notes are available here.

Projects

Prerequisites

Knowledge of probability theory at the level of a basic course, plus preferably a course on random processes. Basic knowledge of Brownian motion is helpful. The computer exercises will be done in Matlab; familiarity with Matlab is thus recommended.

Location and time

The first course week is held at KTH in Stockholm; the second course week is held at Lund University in Lund. Click here for a detailed list of rooms and times.

Social programme and other activities

Accomodation

Contacts

For further information and inquiries, please contact Gustaf Söderlind (046-222 4909, e-mail gustaf@maths.lth.se) or Tobias Rydén (046-222 4778, e-mail tobias@maths.lth.se).

Course homepage

The course homepage is www.maths.lth.se/matstat/research/asn/sdecourse01.html.

Comments or corrections to Tobias Rydén (tobias@maths.lth.se)
Last modified: Sun Sep 30 19:50:48 MEST 2001