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Berry–Esseen Bounds and the Law of the Iterated Logarithm for Estimators of Parameters in an Ornstein–Uhlenbeck Process with Linear Drift

Part of: Stochastic processes Limit theorems Survival analysis and censored data

Published online by Cambridge University Press:  30 January 2018

Hui Jiang
Hui Jiang*
Affiliation:
Nanjing University of Aeronautics and Astronautics
*
∗ Postal address: School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China. Email address: jianghui_1981@hotmail.com
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Abstract

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We study the asymptotic behaviors of estimators of the parameters in an Ornstein–Uhlenbeck process with linear drift, such as the law of the iterated logarithm (LIL) and Berry–Esseen bounds. As an application of the Berry–Esseen bounds, the precise rates in the LIL for the estimators are obtained.

Keywords

Berry–Esseen boundlaw of the iterated logarithmmaximum likelihood estimatorOrnstein–Uhlenbeck processprecise rate

MSC classification

Primary: 62N02: Estimation 60F15: Strong theorems 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 978 - 989
Copyright
© Applied Probability Trust 

Footnotes

Research supported by the National Natural Science Foundation of China under grant 11101210 and by the Fundamental

Research Funds for Nanjing University of Aeronautics and Astronautics under grant NS2010189.

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