Sampling conditioned hypoelliptic diffusions
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.
Cite
@article{arxiv.0908.0162,
title = {Sampling conditioned hypoelliptic diffusions},
author = {Martin Hairer and Andrew M. Stuart and Jochen Voss},
journal= {arXiv preprint arXiv:0908.0162},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP708 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)