Li, LLu, JMattingly, JCWang, L2019-01-232019-01-23https://hdl.handle.net/10161/17916We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and iterated It\^o integrals, the proposed scheme approximates the probability measure $\mu(X^{n+1}|X^n=x_n)$ by a mixture of Gaussians. The solution at next time step $X^{n+1}$ is then drawn from the Gaussian mixture with complexity linear in the dimension $d$. This provides a new general strategy to construct efficient high weak order numerical schemes for SDEs.math.NAmath.NAmath.PR65, 60Journal article2019-01-23