Sampling Paths of SDEs, Conditional on Observations 

Andrew Stuart (Maths Institute, Warwick University)

Joint work with Jochen Voss and Petter Wiberg.

We describe an MCMC method for sampling paths of  SDEs, conditional on observations. Typical examples of observations are point observations of the process at two points (boundary conditions) or a noisy observation of a functional of the path (nonlinear Kalman filter). The approach is to generalize the Langevin sampling technique to infinite dimensions. This is done by discretization, application of the finite dimensional Langevin method, and passage to the limit.