论文标题
部分可观测时空混沌系统的无模型预测
Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime
论文作者
论文摘要
我们研究了应用于随机微分方程的一类多尺度系统的数值方案家族。当时间尺度分离参数消失时，众所周知的同质化或Zakai扩散近似结果表明，所考虑的系统的缓慢分量会收敛到由实现的维纳台过程驱动的随机微分方程的解决方案，并具有对噪声的策略解释。我们提出和分析方案以有效地近似缓慢的成分。这些方案满足了渐近保存财产的满足，并概括了最近一篇文章中提出的方法。我们在分析这些方案的分析中填补了一个空白，并证明了强误差估计值，相对于时间尺度分离参数，它们均匀。
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known homogenization or Wong--Zakai diffusion approximation result states that the slow component of the considered system converges to the solution of a stochastic differential equation driven by a real-valued Wiener process, with Stratonovich interpretation of the noise. We propose and analyse schemes for effective approximation of the slow component. Such schemes satisfy an asymptotic preserving property and generalize the methods proposed in a recent article. We fill a gap in the analysis of these schemes and prove strong error estimates, which are uniform with respect to the time scale separation parameter.
