Stochastic PDEs Arising in Conditional Path Sampling
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
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.
Organisations
Publications
Apte A
(2007)
Sampling the posterior: An approach to non-Gaussian data assimilation
in Physica D: Nonlinear Phenomena
BESKOS A
(2011)
MCMC METHODS FOR DIFFUSION BRIDGES
in Stochastics and Dynamics
Hairer M
(2012)
A spatial version of the Itô-Stratonovich correction
in The Annals of Probability
Hairer M
(2010)
A spatial version of the Itô-Stratonovich correction
Hairer M
(2010)
Approximations to the Stochastic Burgers Equation
Hairer M
(2010)
Singular perturbations to semilinear stochastic heat equations
in Probability Theory and Related Fields
Hairer M
(2010)
Singular perturbations to semilinear stochastic heat equations
Hairer M
(2011)
On Malliavin's proof of Hörmander's theorem
Hairer M
(2009)
Sampling conditioned hypoelliptic diffusions