| ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS |
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| 引用本文： | 胡耀忠,龙红卫.ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS[J].数学物理学报(B辑英文版),2009,29(3):599-608. |
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| 作者姓名： | 胡耀忠 龙红卫 |
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| 作者单位： | Hu Yaozhong(Department of Mathematics, University of Kansas, 605 Snow Hall, Lawrence, Kansas 66045-P142, USA);Long Hongwei(Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA)
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| 基金项目： | 国家自然科学基金，FAU Staxt-up funding at the C. E. Schmidt College of Science |
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| 摘 要： | We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in 7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.
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| 关 键 词： | 最小二乘估计 稳定运动 奇异性 回复 平均 参数估计 离散时间 遍历 |
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