Analysis of SPDEs arising in Path Sampling, Part I: The Gaussian Case

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details: , , and : Analysis of SPDEs arising in Path Sampling, Part I: The Gaussian Case. Communications in Mathematical Sciences, vol. 3, no. 4, pp. 587–603, 2005.
online: link, journal
preprint: arXiv:math/0601095, preprint:pdf, preprint:ps
metadata: BibTeX, MathSciNet, Google
keywords: SPDEs, conditioned diffusions, Gaussian Processes, Kalman filter, high dimensional sampling
MSC2000: 60H15, 60G15, 60G35, 60H10

Abstract

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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