Statistical Romberg Extrapolation: A Novel Acceleration Algorithm for The Discretization of Forward Backward Stochastic Differential Equations

We introduce the statistical Romberg extrapolation method, a novel acceleration technique for discretizing forward backward stochastic differential equations. Compared to the classical Crank-Nicolson scheme, our single-step method achieves third-order convergence, which is significantly higher than the second-order convergence exhibited by the classical Crank-Nicolson scheme. Precise error estimates are derived, rigorously establishing this third-order convergence rate. Numerical experiments confirm the analysis and demonstrate a substantial improvement in accuracy.