| Boltzmann-Gibbs Preserving Langevin Integrators (2007) | |||||||||
Abstract | |||||||||
| This paper analyses a class of structure-preserving Langevin integrators obtained from a Lie-Trotter splitting of the Langevin equations into Hamilton's and Ornstein-Uhlenbeck equations. The schemes are defined as a composite map $\phi_h = \theta_h \circ \phi_h$ where $\theta_h$ is a pth-order accurate symplectic integrator for Hamilton's equations and $\phi_h$ is the exact solution of the Ornstein-Uhlenbeck equations. The paper shows this composite map is consistent with Langevin equations and locally preserves the Boltzmann-Gibbs measure to $(p+1)th$ order ($p \ge 1$). Moreover, when the underlying Langevin process is geometrically ergodic, the paper shows the discrete invariant measure of $\phi_h$ is about $pth$-order in the TV norm.. Comment: 18 pages, 8 figures | |||||||||
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