选择非线性随机微分方程模型的最优Strang分裂估计器
Choosing optimal Strang splitting estimators of nonlinear stochastic differential equation models
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中文总结 AI 辅助
研究在非线性随机微分方程模型中如何选择最优Strang分裂估计器，推导其转移密度误差度量，通过模拟研究发现定点附近线性化对势模型、其他分裂对快慢可激发模型能产生更好的参数估计。
中文摘要 AI 辅助
Strang分裂估计器是用于具有非线性漂移和加性噪声的多元随机微分方程模型参数推断的强大估计器。虽然分裂的选择不影响估计器的渐近分布，但在有限样本设置中有巨大影响，且尚未表明如何最优选择分裂。我们推导了Strang分裂方案转移密度的误差度量，特别是计算了高达$h^3$阶的偏差，其中$h$是时间步长。我们分别研究了这些误差度量与双阱势模型和随机FitzHugh-Nagumo模型中Strang分裂估计器性能之间的联系。我们的模拟研究表明，定点附近的线性化对势模型产生准确的参数估计，而其他分裂对快慢可激发模型表现更好。
英文摘要
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.
