The Annals of Applied Probability

Sampling conditioned hypoelliptic diffusions

Martin Hairer, Andrew M. Stuart, and Jochen Voss

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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.

Article information

Ann. Appl. Probab. Volume 21, Number 2 (2011), 669-698.

First available in Project Euclid: 22 March 2011

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Stochastic partial differential equations fourth-order SPDEs hypoelliptic diffusions conditioned stochastic ordinary differential equations


Hairer, Martin; Stuart, Andrew M.; Voss, Jochen. Sampling conditioned hypoelliptic diffusions. Ann. Appl. Probab. 21 (2011), no. 2, 669--698. doi:10.1214/10-AAP708.

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