Nested multilevel Monte Carlo methods and a modified Euler-Maruyama scheme utilising approximate Gaussian random variables suitable for vectorised hardware and low-precisions - Sheridan-Methven, O (2021)
We present a modified Euler-Maruyama scheme using approximate random variables, produced by the inverse transform method, using cheap approximations to the inverse Gaussian cumulative distribution function. We analyse the error for two approximations: a piecewise constant approximation on equally spaced intervals, and a piecewise linear approximation using geometric intervals dense at the singularities. High speed implementations faster than Intel's MKL are provided, suitable for modern vector hardware. The error between the approximations from the exact and modified Euler-Maruyama schemes is bounded by the error from the approximate random variables.