Open Access
December 2005 Analysis of SPDEs arising in path sampling. Part I: The Gaussian case
M. Hairer, A. M. Stuart, J. Voss, P. Wiberg
Commun. Math. Sci. 3(4): 587-603 (December 2005).


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.


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M. Hairer. A. M. Stuart. J. Voss. P. Wiberg. "Analysis of SPDEs arising in path sampling. Part I: The Gaussian case." Commun. Math. Sci. 3 (4) 587 - 603, December 2005.


Published: December 2005
First available in Project Euclid: 7 April 2006

zbMATH: 1138.60326
MathSciNet: MR2188686

Primary: 60H15
Secondary: 60G15 , 60G35 , 60H10

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 4 • December 2005
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