Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero. The rate of convergence is presented when coefficients are Hölder continuous. Monte Carlo simulations are also discussed.
"The Euler scheme with irregular coefficients." Ann. Probab. 30 (3) 1172 - 1194, July 2002. https://doi.org/10.1214/aop/1029867124