Local linear estimator for stochastic differential equations driven by $α$-stable Lévy motions

Details Local linear estimator for stochastic differential equations driven by $α$-stable Lévy motions Local linear estimator for stochastic differential equations driven by $α$-stable Lévy motions

2012-04-06

arxiv.org/abs/1204.1454v1

Mathematics

Statistics Theory

15 pages

Scientific paper

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.

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