Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations

Nawaf Bou-Rabee

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arXiv · 1707.05603

Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations

Nawaf Bou-Rabee

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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.

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BibTeX RIS

Nawaf Bou-Rabee. 2017-07-18. Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations. https://arxiv.org/abs/1707.05603

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