The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.

中文翻译：

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随机哈密顿系统的保漂移数值积分器

本文讨论了具有加性噪声的可分离非线性哈密顿系统的数值离散化。对于此类问题，总能量的期望值会沿着精确的解决方案随时间线性漂移。我们介绍并分析一个在任何时候都具有相同属性的时间积分器。此外，还研究了数值方案的强弱收敛以及有效的多层蒙特卡洛估计。最后，大量的数值实验说明了所提出数值方案的性能。