Publications [#358291] of Jonathan C. Mattingly

Papers Published

1. Li, L; Lu, J; Mattingly, JC; Wang, L, Numerical Methods For Stochastic Differential Equations Based On Gaussian Mixture, Communications in Mathematical Sciences, vol. 19 no. 6 (January, 2021), pp. 1549-1577, International Press of Boston [doi]
   (last updated on 2025/01/30)

   Abstract:
   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