Abstract In this paper, we are concerned with strong convergence rate of Euler scheme for time-inhomogeneous one-dimensional stochastic differential equations involving the local time (SDELT) of the unknown process at point zero. We use a space transform in order to remove the local time from this class of stochastic differential equations. We provide the approximation of Euler for the stochastic differential equation without local time. After that the approximation can be transformed back, giving an approximation of Euler to the solution of the original SDELT, and we provide the rate of strong convergence.

中文翻译：

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涉及未知过程本地时间的时间非齐次 SDE 的 Euler 格式收敛率

摘要 在本文中，我们关注的是时间非齐次一维随机微分方程的 Euler 格式的强收敛速度，该方程涉及未知过程在零点的本地时间（SDELT）。我们使用空间变换来从这类随机微分方程中去除本地时间。我们提供了无本地时间的随机微分方程的欧拉近似。之后，可以将近似值转换回来，给出原始 SDELT 解的欧拉近似值，我们提供强收敛率。