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.

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)

References in corpus (4)

• An Introduction to Stochastic PDEs
• Noisy Kuramoto-Sivashinsky equation for an erosion model
• Analysis of SPDEs arising in path sampling part II: The nonlinear case
• Singular perturbations to semilinear stochastic heat equations

Cited by in corpus (5)

• Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion
• Simulation of elliptic and hypo-elliptic conditional diffusions
• Simulation of forward-reverse stochastic representations for conditional diffusions
• Optimal friction matrix for underdamped Langevin sampling
• Singular perturbations to semilinear stochastic heat equations