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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.
ISSN 1050-5164

**Full text not available from this repository.**

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 > 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 |

Volume: | Volume 21 |

Number: | Number 2 |

Page Range: | pp. 669-698 |

Identification Number: | 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) |

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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