Analysis of SPDEs arising in path sampling. I: The Gaussian case. (English) Zbl 1138.60326

Hairer, M.; Stuart, A. M.; Voss, J.; Wiberg, P.

Commun. Math. Sci. 3, No. 4, 587-603 (2005).

Summary: In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. Here the theory is developed for conditioned Gaussian processes for which the resulting SPDE is linear. Applications include the Kalman-Bucy filter/smoother. A companion paper studies the nonlinear case, building on the linear analysis provided here.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60G15	Gaussian processes
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60G35	Signal detection and filtering (aspects of stochastic processes)