Strong rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero

We present the Euler-Maruyama approximation for one-dimensional stochastic differential equations involving the local time at point zero. Also, we prove the strong convergence of the Euler-Maruyama approximation whose both drift and diffusion coefficients are Lipschitz. After that, we generalize to the non-Lipschitz case.