Objective

Stochastic Differential Equations (SDEs) have become a quite standard tool to model differential equation systems subject to noise. Applications range from Neuroscience or Polymeric Chemistry to Finance or Mechanical Engineering. Treating practical problems requires analytic techniques to understand and investigate properties of SDEs and stochastic numerical methods to compute quantities of interest, where the latter and the former often go hand in hand. This course provides a basic inroduction to the concepts of SDEs and how to develop and analyse numerical methods for their simulation.

Assumed prior knowledge: Standard analysis and linear algebra, Numerical analysis of ordinary differential equations (including the corresponding programming skills), Basic probability theory.

Contents

• Introduction to Brownian motion, the Ito integral and SDEs;
• Basic stochastic simulation;
• Numerical methods for SDEs: what do they compute and what does convergence mean here?
• How to develop numerical methods for SDEs and a few classical examples
• Basic issues in analysing the performance of the methods.

This material will be provided in lectures and exercise classes, which include implementing numerical methods and testing them.

Examination format

Written report on a project.

Schedule

• Week 36: 2 x 2 hours lecture plus 1 hour Exercies
• Week 38: 2 x 2 hours lecture plus 1 hour Exercies
• Week 40: 2 x 2 hours lecture plus 1 hour Exercies
• Week 41: 2 x 2 hours lecture plus 1 hour Exercies
• Week 42: 1 x 2 hours lecture plus 1 hour Exercies/Projectpresentation

Personnel

• Course coordinator: Philipp Birken
• Lecturer: Evelyn Buckwar

Registration

Registration is now closed.

Registration deadline: 26 August 2022