Sampling conditioned hypoelliptic diffusions

摘要: A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect the distribution given conditioned diffusion. These works restricted case elliptic diffusions where drift has gradient structure and resulting SPDE is second-order parabolic type. The present article extends this methodology allow construction SPDEs class hypoelliptic diffusion processes, subject bridge conditioning, leading fourth-order type. This allows treatment more realistic physical models, for example, one can use study transitions between meta-stable states in mechanical systems friction noise. In situation restriction being also be lifted.