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Sampling conditioned hypoelliptic diffusions
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Hairer, Martin, Stuart, A. M. and Voss, Jochen (2011) Sampling conditioned hypoelliptic diffusions. The Annals of Applied Probability, Volume 21 (Number 2). pp. 669-698. doi:10.1214/10-AAP708 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/10-AAP708
Abstract
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type.
The present article extends this methodology to allow the construction of SPDEs which are invariant with respect to the distribution of a class of hypoelliptic diffusion processes, subject to a bridge conditioning, leading to SPDEs which are of fourth-order parabolic type. This allows the treatment of more realistic physical models, for example, one can use the resulting SPDE to study transitions between meta-stable states in mechanical systems with friction and noise. In this situation the restriction of the drift being a gradient can also be lifted.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Diffusion processes | ||||
| Journal or Publication Title: | The Annals of Applied Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 1050-5164 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Volume 21 | ||||
| Number: | Number 2 | ||||
| Page Range: | pp. 669-698 | ||||
| DOI: | 10.1214/10-AAP708 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC) | ||||
| Grant number: | EP/E002269/1 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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