AI 中文总结
针对不变域为开有界区间的标量随机微分方程，提出用Lamperti变换结合正则性假设构建高阶保边界数值格式以强逼近，经数值实验验证该方法能实现所需收敛阶。
AI 中文摘要
在这项工作中，我们为一些不变域为开有界区间的标量随机微分方程的强逼近提出了高阶保边界数值格式。所提出的方法包括使用Lamperti变换将随机微分方程映射到另一个具有平凡不变域且带有加性噪声的随机微分方程。然后，通过对原始系数函数施加正则性假设，我们可以保证变换后的随机微分方程的漂移系数函数是正则的，并且可以使用已知的高阶格式来实现所需的收敛阶。我们通过数值实验证实了理论结果。
英文摘要
In this work, we propose high-order boundary-preserving numerical schemes for the strong approximation for some scalar stochastic differential equations with invariant domains being open and bounded intervals. The proposed methods involve using the Lamperti transform to map the SDE to another SDE with additive noise with a trivial invariant domain. Then, by imposing regularity assumptions on the original coefficient functions, we can guarantee that the drift coefficient function of the transformed SDE is regular, and known high-order schemes can be used to achieve the desired convergence order. We confirm the theoretical results with numerical experiments.
Comments26 pages, 6 figures
