Sampling conditioned hypoelliptic diffusions
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. ISSN 1050-5164Full text not available from this repository.
Official URL: http://dx.doi.org/10.1214/10-AAP708
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 > 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|
|Page Range:||pp. 669-698|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)|
|Grant number:||EP/E002269/1 (EPSRC)|
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