最小二乘估计：受莱维噪声扰动的随机微分方程的稀疏样本路径
Least Square Estimation: SDEs Perturbed by Lévy Noise with Sparse Sample Paths
AI总结：
本文提出了一种针对受莱维噪声扰动的随机微分方程中稀疏样本路径的最小二乘估计方法，并分析了其渐近收敛速率。
摘要：
本文研究了受莱维噪声影响的随机微分方程（SDEs）中未知参数的最小二乘估计（LSE）。具体而言，给定n条稀疏观测曲线，我们推导出未知参数的最小二乘估计：漂移系数、扩散系数和跳跃扩散系数。我们还建立了所提LSE估计量的渐近收敛速率。此外，在补充材料中，所提方法应用于功能数据/曲线的基准数据集，并进行了小规模模拟研究以说明结果。
英文摘要：
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by Lévy noise, particularly when the sample paths are sparse. Specifically, given $n$ sparsely observed curves related to this model, we derive the least squares estimators for the unknown parameters: the drift coefficient, the diffusion coefficient, and the jump-diffusion coefficient. We also establish the asymptotic rate of convergence for the proposed LSE estimators. Additionally, in the supplementary materials, the proposed methodology is applied to a benchmark dataset of functional data/curves, and a small simulation study is conducted to illustrate the findings.
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