Numerical Methods For Stochastic Differential Equations Based On Gaussian Mixture

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second-order accuracy based on Gaussian mixture. Unlike conventional higher order schemes for SDEs based on Itô-Taylor expansion and iterated Itô integrals, the scheme we propose approximates the probability measure μ(Xn+1|Xn =xn) using a mixture of Gaussians. The solution at the next time step Xn+1 is drawn from the Gaussian mixture with complexity linear in dimension d. This provides a new strategy to construct efflcient high weak order numerical schemes for SDEs

Duke Scholars

Author Jianfeng Lu Mathematics

Author Jonathan Christopher Mattingly Mathematics