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Methodology and Computing in Applied Probability

, Volume 21, Issue 4, pp 1165–1182 | Cite as

The Least Squares Estimation for the α-Stable Ornstein-Uhlenbeck Process with Constant Drift

  • Yurong Pan
  • Litan YanEmail author
Article

Abstract

In this paper, we consider the least squares estimators of the Ornstein-Uhlenbeck process with a constant drift
$$dX_{t}=(\theta_{1}-\theta_{2}X_{t})dt+dZ_{t} $$
with X0 = x0, where θ1, θ2 are two unknown parameters with θ2 > 0 and Z is a strictly symmetric α-stable motion on ℝ with the index α ∈ (1, 2). We construct the least squares estimators of θ1 and θ2 based on the discrete observation, and discuss the strong consistency and asymptotic distributions of the two estimators. Finally, we give some numerical calculus and simulations.

Keywords

Least squares estimation Ornstein-Uhlenbeck process α-stable motion Consistency Asymptotic distribution 

Mathematics Subject Classification (2010)

60H10 60F15 60G52 

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Notes

Acknowledgments

The Project-sponsored by NSFC (11571071), Key Natural Science Foundation of Anhui Education Commission(KJ2017A568, KJ2016A453), KYTD(BBC2016-02), and AHSKQ2016D29, and Natural Science Foundation of Anhui Province (1808085MA02).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Science, Department of MathematicsBengbu UniversityBengbuPeople’s Republic of China
  2. 2.Department of Mathematics, College of ScienceDonghua UniversityShanghaiPeople’s Republic of China

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