论文标题
随机$θ$ -METHODS的均值合同
Mean-square contractivity of stochastic $θ$-methods
论文作者
论文摘要
该论文的重点是随机$θ$ - 方法的非线性稳定性分析。特别是，我们考虑了非线性随机微分方程，以使两种溶液之间的均方偏差成倍衰减，即沿随机动力学可见均方相关行为。我们的目标是使同一属性也可以沿由随机$θ$ -Methods生成的数值动力学可见：此问题根据问题的参数而转化为急剧的步骤限制，此处是准确估计的。还提供了确认分析及其清晰度的有效性的数值测试的选择。
The paper is focused on the nonlinear stability analysis of stochastic $θ$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays, i.e., a mean-square contractive behaviour is visible along the stochastic dynamics. We aim to make the same property visible also along the numerical dynamics generated by stochastic $θ$-methods: this issue is translated into sharp stepsize restrictions depending on parameters of the problem, here accurately estimated. A selection of numerical tests confirming the effectiveness of the analysis and its sharpness is also provided.
