Open Access
April 2011 Sampling conditioned hypoelliptic diffusions
Martin Hairer, Andrew M. Stuart, Jochen Voss
Ann. Appl. Probab. 21(2): 669-698 (April 2011). DOI: 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.


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Martin Hairer. Andrew M. Stuart. Jochen Voss. "Sampling conditioned hypoelliptic diffusions." Ann. Appl. Probab. 21 (2) 669 - 698, April 2011.


Published: April 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1219.60062
MathSciNet: MR2807970
Digital Object Identifier: 10.1214/10-AAP708

Primary: 60H15
Secondary: 60G35

Keywords: conditioned stochastic ordinary differential equations , fourth-order SPDEs , Hypoelliptic diffusions , Stochastic partial differential equations

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.21 • No. 2 • April 2011
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