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Numerical treatment of stochastic functional differential equations

Objective



Research objectives and content In this project stochastic functional differential equations (SFDEs) will be considered. These equations play an important role in modelling f.e. population dynamics, stochastic control systems and investment financing, when time delays and stochastic effects have to be taken into account. The analytical theory of SFDEs is relatively well developed, as is the analytical and numerical theory of deterministic functional differential equations (FDEs) and stochastic ordinary differential equations (SODEs). The aim of my project is to develop and analyse numerical methods to solve SFDEs with special emphasis on stochastic delay differential equations (SDDEs). I want to investigate how methods used for FDEs and SODEs can be brought together to yield methods for SFDEs. The objective is to seek a collection of representative model equations with well-known SODE and FDE counterparts and to provide a robust adaptive code for that class of SFDEs. The programmepackage will be made available via internet. Training content (objective, benefit and expected impact) I will gain from the considerable expertise in Manchester on the numerical solution of ordinary and delay differential equations, which for me is a new area of research. Furthermore I can benefit from the fact that the group has links with workers on stochastic equations. I will get experience in a relatively new, but important (espesially with regard to more precise modelling) area of research. Links with industry / industrial relevance (22)

Coordinator

UNIVERSITY OF MANCHESTER
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M13 9PL Manchester
United Kingdom