• DOI:10.1214/10-AAP708
• Corpus ID: 10850143

Sampling conditioned hypoelliptic diffusions

@article{Hairer2009SamplingCH,
  title={Sampling conditioned hypoelliptic diffusions},
  author={Martin Hairer and Andrew M. Stuart and Jochen Voss},
  journal={Annals of Applied Probability},
  year={2009},
  volume={21},
  pages={669-698}
}

• Martin Hairer, A. Stuart, J. Voss
• Published 2 August 2009
• Mathematics
• Annals of Applied Probability

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.