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.

翻译：本文研究了受Lévy噪声影响的随机微分方程（SDE）中未知参数的最小二乘估计量（LSE），特别关注样本路径稀疏的情况。具体而言，给定与该模型相关的$n$条稀疏观测曲线，我们推导了未知参数（漂移系数、扩散系数和跳跃扩散系数）的最小二乘估计量。同时，我们建立了所提出LSE估计量的渐近收敛速率。此外，在补充材料中，将所提出的方法应用于函数数据/曲线的基准数据集，并通过小型模拟研究验证了研究结果。