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
(2010)
Singular perturbations to semilinear stochastic heat equations
in Probability Theory and Related Fields
Hairer M
(2013)
Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
in The Annals of Probability
Hairer M
(2011)
On Malliavin's proof of Hörmander's theorem
in Bulletin des Sciences Mathématiques
Hairer M
(2010)
Rough Stochastic PDEs
Hairer M
(2011)
Approximations to the Stochastic Burgers Equation
in Journal of Nonlinear Science
Hairer M
(2007)
Analysis of SPDEs arising in path sampling part II: The nonlinear case
in The Annals of Applied Probability