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In this paper, we consider the weak convergence of the Euler-Maruyamaapproximation for one dimensional stochastic differential equations involvingthe local times of the unknown process. We use a transformation in order toremove the local time from the stochastic differential equations and we providethe approximation of Euler-maruyama for the stochastic differential equationswithout local time. After that, we conclude the approximation of Euler-maruyamafor one dimensional stochastic differential equations involving the local timesof the unknown process , and we provide the rate of weak convergence for anyfunction G in a certain class.

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