论文标题
随机泊松系统的漂移保存数值集成符
Drift-preserving numerical integrators for stochastic Poisson systems
论文作者
论文摘要
我们对一类随机扰动{H} Amiltonian Systems和{P} Oisson Systems进行数值分析。对于此类系统的考虑的附加噪声扰动，我们显示了精确解决方案的能量和二次casimirs的长时间行为。然后，我们提出并分析了具有以下特性的此类问题的漂移保护方案：能量和二次Casimirs的精确漂移保存，均值收敛的均值顺序，弱收敛顺序二。这些特性通过数值实验说明。
We perform a numerical analysis of a class of randomly perturbed {H}amiltonian systems and {P}oisson systems. For the considered additive noise perturbation of such systems, we show the long time behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence one, weak order of convergence two. These properties are illustrated with numerical experiments.
