Communications in Mathematical Sciences

Analysis of SPDEs arising in path sampling. Part I: The Gaussian case

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

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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.

Article information

Commun. Math. Sci., Volume 3, Number 4 (2005), 587-603.

First available in Project Euclid: 7 April 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60G15: Gaussian processes 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60H10: Stochastic ordinary differential equations [See also 34F05]


Hairer, M.; Stuart, A. M.; Voss, J.; Wiberg, P. Analysis of SPDEs arising in path sampling. Part I: The Gaussian case. Commun. Math. Sci. 3 (2005), no. 4, 587--603.

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