Hairer, M. and Stuart, A. M. and Voss, J. and Wiberg, P. (2005) Analysis of SPDEs arising in path sampling. Part I: The Gaussian case. Communications in Mathematical Sciences, 3 (4). pp. 587-603. ISSN 1539-6746. doi:10.4310/CMS.2005.v3.n4.a8. https://resolver.caltech.edu/CaltechAUTHORS:20170612-141658808
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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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| Additional Information: | © 2005 International Press. Received: September 1, 2005; accepted (in revised version): October 14, 2005. Supported by Marie Curie Fellowship HPMT-CT-2000-00076. | ||||||||||||
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| Issue or Number: | 4 | ||||||||||||
| Classification Code: | 2010 Mathematics Subject Classification: Primary 60H15. Secondary 60G15, 60G35, 60H10 | ||||||||||||
| DOI: | 10.4310/CMS.2005.v3.n4.a8 | ||||||||||||
| Record Number: | CaltechAUTHORS:20170612-141658808 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170612-141658808 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 78121 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 12 Jun 2017 21:39 | ||||||||||||
| Last Modified: | 15 Nov 2021 17:36 |
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