Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations
Probability
2017-07-19 v1 Numerical Analysis
Abstract
We give accurate and ergodic numerical methods for semilinear, second-order Langevin stochastic partial differential equations (SPDE). As a byproduct, we also give good geometric numerical methods for their infinite-dimensional Hamiltonian counterpart. These methods are suitable for Hamiltonian Monte Carlo on Hilbert spaces without preconditioning the underlying Hamiltonian dynamics. A key tool in our approach is Krein's theory on strong stability of symplectic maps, which gives us sufficient conditions for stability of symplectic splitting schemes in highly oscillatory Hamiltonian problems.
Cite
@article{arxiv.1707.05603,
title = {Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations},
author = {Nawaf Bou-Rabee},
journal= {arXiv preprint arXiv:1707.05603},
year = {2017}
}
Comments
65 pages, 34 figures