迭代Taylor方法的随机B-级数分析
Stochastic B-series analysis of iterated Taylor methods
AI总结：
针对使用迭代方案计算数值解的随机隐式Taylor方法，构建随机B-级数及相应增长函数，并基于底层Taylor方法的阶数、迭代方法选择、预测子和迭代次数，推导Itô和Stratonovich SDE的弱收敛与强收敛结果。
摘要：
对于使用迭代方案计算数值解的随机隐式Taylor方法，构建了随机B-级数及相应的增长函数。由此，基于底层Taylor方法的阶数、迭代方法的选择、预测子和迭代次数，推导了Itô和Stratonovich SDE的弱收敛和强收敛结果。作为特例，还考虑了Taylor方法在ODE中的应用。该理论得到了数值实验的支持。
英文摘要：
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor and the number of iterations, for Itô and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments.
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