Parameter estimation with SSSDE: Splitting Schemes for Stochastic Differential Equations

This talk presents two efficient and easy-to-implement likelihood-based estimators for nonlinear continuous time models based on stochastic differential equations (SDEs). These estimators are obtained from the Lie-Trotter (LT) and Strang (S) splitting schemes, numerical approximations that preserve the geometrical properties of an SDE. We show that both estimators are consistent and asymptotically normal under the less restrictive one-sided Lipschitz assumption. In addition, we show that the S estimator has an Lp convergence rate of order 1 and provide a numerical study on the 3-dimensional stochastic Lorenz chaotic system, which demonstrates that the S estimator outperforms existing state-of-the-art methods in terms of precision and computational speed. Our implementation relies on automatic differentiation, making it faster and easier to use than existing methods based on numerical differentiation.