Geometric integration of stochastic differential equations

Project description

The project belongs to the following areas of Mathematics: Stochastic Analysis, Applied Probability, Numerical Analysis

For many applications (especially, in molecular dynamics and Bayesian statistics), it is of interest to compute the mean of a given function with respect to the invariant law of the diffusion, i.e. the ergodic limit. To evaluate these mean values in situations of practical interest, one has to integrate large dimensional systems of stochastic differential equations over long time intervals.  Computationally, this is a challenging problem.   Stochastic geometric integrators play an important role in long-time simulation of dynamical systems with high accuracy and relatively low cost.  The project can be on the rapidly growing area of numerical approximation of SDEs on manifolds.

The project involves construction of new efficient numerical methods for ergodic stochastic differential equations and stochastic numerical analysis of properties of the methods.

We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). We are expecting that the successful applicant has a very good background in Probability and has good computational skills.