Details of Grant 

EPSRC Reference:	EP/E002269/1
Title:	Stochastic PDEs Arising in Conditional Path Sampling
Principal Investigator:	Hairer, Professor M
Other Investigators:	Stuart, Professor A
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Warwick
Scheme:	Standard Research
Starts:	31 March 2007	Ends:	30 March 2010	Value (£):	198,836
EPSRC Research Topic Classifications:	Mathematical Analysis Numerical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
We analyze a stochastic PDE (SPDE) based approach to sampling paths of SDEs, conditional on observations. The SPDEs are derived by generalizing the Langevin equation to infinite dimensions. Problems which can be tackled by this methodology include the sampling of paths subject to two end-point conditions (bridges) and nonlinear filter/smoothers. Applications include rare event sampling in molecular systems, econometrics, data assimilation and signal processing. The aims of the proposal are: (i) to put the subject on a firm theoretical foundation, by studying the existence, uniqueness, regularity and ergodicity of the resulting SPDEs; (ii) to develop a theoretical understanding of effective computational algorithms, based on the path space density giving rise to the SPDEs, by combining discretization and MCMC methods.
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Organisation Website:	http://www.warwick.ac.uk