Local linear estimator for stochastic differential equations driven by $\alpha$-stable L\'{e}vy motions

TL;DR

This paper develops a local linear estimator for the drift coefficient in SDEs driven by alpha-stable Lévy motions, demonstrating its consistency, asymptotic normality, and bias reduction advantages over Nadaraya-Watson estimators.

Contribution

It introduces a novel local linear estimation method for SDEs with alpha-stable Lévy noise, providing theoretical properties and bias reduction insights.

Findings

Estimator is weakly consistent and asymptotically normal.

Local linear estimator reduces bias compared to Nadaraya-Watson.

Method applies under regular conditions for discretely observed data.

Abstract

We study the local linear estimator for the drift coefficient of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motions observed at discrete instants letting $T \rightarrow \infty$. Under regular conditions, we derive the weak consistency and central limit theorem of the estimator. Compare with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether kernel function is symmetric or not under different schemes.