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Cubature on Wiener space, recombination of particle measures and applications

   Department of Mathematics

  Dr Christian Litterer  Applications accepted all year round  Funded PhD Project (UK Students Only)

About the Project

This project is devoted to problems that arise when combining the promising and novel approach of ‘cubature on Wiener space’ developed by Kusuoka, Lyons and Victoir with recombination algorithms that can simplify particle descriptions of an evolving system. The aim is to develop powerful numerical methods that can be adopted by practitioners.

The project is rooted in stochastic analysis, but many of the problems arising are at an interface to numerical analysis, (applied algebraic) geometry and algebra and can be developed in several different directions.

We are particularly interested in the following classes of problems:

  • Systematic constructions of high degree cubature measures on Wiener space.
  • The design and analysis of enhanced recombination algorithms that can be used to simplify the support of particle approximations of evolving systems.
  • The application of cubature ideas to develop a high-order approximation of non-linear filtering problems, where one makes inferences about the evolution of complex phenomena based on partial observations of the system. Non-linear filtering problem arise in many practical applications ranging from the focus of a camera in a mobile tracking a moving object, via the imaging produced by a modern MRI scanner in hospital, to the prediction of next week's weather by means of a supercomputer.
  • Applications of the developed algorithms to problems arising in mathematical finance informed by our external project partners with broad experience in the financial services industry.

Applicants should either have some knowledge of a high-level programming language such as C++ or be willing to develop such skills as part of their PhD.

The stochastic analysis and mathematical finance group in York is active in several research areas including the analysis of SPDEs, rough paths and statistical mechanics.

Funding Notes

The start time for the studentship is flexible between March and September 2022. Applications are open to students worldwide. The project is related to the research of our EPSRC grant EP/V005413/1 and may involve some collaboration with our external project partner Prof Terry Lyons FRS who is based in Oxford.

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