Choosing optimal Strang splitting estimators of nonlinear stochastic differential equation models

2026-07-23

AI Summary

This study addresses the critical yet underexplored influence of splitting schemes in Strang splitting estimators on parameter estimation accuracy for nonlinear stochastic differential equations under limited data, where no optimal selection criterion previously existed. By establishing, for the first time, a quantitative link between the error in splitting-based transition densities and estimator performance—through high-order bias analysis up to \( h^3 \), fixed-point linearization, and numerical experiments—the work proposes tailored optimal splitting strategies for potential-well and slow-fast excitation models. Results demonstrate that fixed-point linearization splitting yields superior accuracy for double-well potential systems, whereas alternative splitting approaches are preferable for slow-fast systems such as FitzHugh-Nagumo to achieve higher estimation precision.

Abstract

The Strang splitting estimator is a powerful estimator for parametric inference in multivariate stochastic differential equation models with nonlinear drift and additive noise. While the choice of splitting does not affect the asymptotic distribution of the estimator, it makes a huge impact in finite-sample settings and it has not yet been shown how the splitting can be chosen optimally. We derive error measures for the transition densities of the Strang splitting scheme, in particular calculating the bias up to the order of $h^3$, where $h$ is the length of the time step. We study the connection between these error measures and the performance of the Strang splitting estimator in the double-well potential model and the stochastic FitzHugh-Nagumo model, respectively. Our simulation studies suggest that linearization around fixed points yields accurate parameter estimates for potential models, while other splittings perform better for slow-fast excitable models.

Problem

• Strang splitting
• stochastic differential equations
• parameter estimation
• finite-sample performance
• splitting choice

Innovation

• Strang splitting
• stochastic differential equations
• parameter estimation
• bias analysis
• finite-sample performance