Least Square Estimation: SDEs Perturbed by Lévy Noise with Sparse Sample Paths

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.