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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. 669698. ISSN 10505164
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Official URL: http://dx.doi.org/10.1214/10AAP708
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 secondorder 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 fourthorder parabolic type. This allows the treatment of more realistic physical models, for example, one can use the resulting SPDE to study transitions between metastable 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 > 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:  10505164  
Official Date:  2011  
Dates: 


Volume:  Volume 21  
Number:  Number 2  
Page Range:  pp. 669698  
Identification Number:  10.1214/10AAP708  
Status:  Peer Reviewed  
Publication Status:  Published  
Funder:  Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)  
Grant number:  EP/E002269/1 (EPSRC)  
References:  [1] APTE, A., HAIRER, M., STUART, A. M. and VOSS, J. (2007). Sampling the posterior: An 

URI:  http://wrap.warwick.ac.uk/id/eprint/41615 
Data sourced from Thomson Reuters' Web of Knowledge
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