A note on the Euler-Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient
It is shown that the Euler-Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic differential equation with the same initial condition. The proof uses upper and lower solutions of the stochastic differential equations and the Euler-Maruyama scheme.
euler-maruyama scheme discontinuous monotone drift upper and lower solutions