Euler–Maruyama method

Summary

The Euler–Maruyama method is the simplest numerical scheme for stochastic differential equations. It extends the Euler method for ordinary differential equations by adding, at each step, the diffusion coefficient times a Brownian increment. Under Lipschitz and growth conditions on the coefficients, it converges with strong order $1/2$. Under further smoothness conditions, it converges with weak order $1$.