Least Square Estimation: SDEs Perturbed by L\'evy Noise with Sparse Sample Paths
Methodology
2026-01-01 v1
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 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.
Cite
@article{arxiv.2512.24005,
title = {Least Square Estimation: SDEs Perturbed by L\'evy Noise with Sparse Sample Paths},
author = {Brijesh Kumar Jha and Subhra Sankar Dhar and Akash Ashirbad Panda},
journal= {arXiv preprint arXiv:2512.24005},
year = {2026}
}