标题： 一维随机微分方程的欧拉-马鲁耶姆逼近的弱收敛率，涉及未知过程的局部时间 显示英文标题

标题： The weak rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local times of the unknown process

摘要： 在本文中，我们考虑一维随机微分方程中欧拉-马鲁耶姆近似关于局部时间的弱收敛性。 我们使用一种变换来消除随机微分方程中的局部时间，并为没有局部时间的随机微分方程提供欧拉-马鲁耶姆的近似。 之后，我们得出涉及未知过程局部时间的一维随机微分方程的欧拉-马鲁耶姆近似，并为某一类中的任何函数G提供弱收敛速率。 显示英文摘要

摘要： In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local time from the stochastic differential equations and we provide the approximation of Euler-maruyama for the stochastic differential equations without local time. After that, we conclude the approximation of Euler-maruyama for one dimensional stochastic differential equations involving the local times of the unknown process , and we provide the rate of weak convergence for any function G in a certain class.