The COMPUTE course "Advanced material on Stochastic Numerics" (3 ECTS) is now open for registration.  The course will run during 7-11 September, 2020 and will be entirely online.  Details of the course content can be found below and on the COMPUTE webpage. The application form can be found here.

Students must be COMPUTE members to take this course: Membership is free, comes without any obligatory courses etc., and is open to all PhD students at the faculties of Science, Medicine, and LTH. The membership application form can be downloaded here.

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Advanced Material on Stochastic Numerics (3 ECTS)

Stochastic Differential Equations (SDEs) have become a 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. During this course we will discuss efficiency of Monte Carlo methods for SDEs
and how to improve it by variance reduction techniques and Multi-level Monte Carlo, and we will explore structural properties of SDEs and numerical methods that preserve these properties.

Contents:

• Recap of SDEs and numerical methods for SDEs.
• Monte Carlo methods for SDEs: Weak approximations for SDEs and their efficiency
• Variance reduction techniques and Multi-level Monte Carlo
• Structural properties for SDEs
• Numerical methods that preserve structural properties, in particular splitting methods

The material will be provided in lectures and exercise classes, which include implementing numerical methods and testing them. The course will take place online.