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