Least Square Estimation: SDEs Perturbed by L\'evy Noise with Sparse Sample Paths

TL;DR

This paper develops least squares estimators for parameters in Le9vy-noise-perturbed SDEs with sparse data, establishing their convergence rates and demonstrating their effectiveness through simulations and a benchmark dataset.

Contribution

It introduces a novel least squares estimation method for SDEs with Le9vy noise under sparse sampling, including asymptotic analysis and practical validation.

Findings

Established convergence rates for the estimators.

Validated the methodology with simulations.

Applied the approach to real functional data.

Abstract

This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy 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.