ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

doi:10.1016/S0252-9602(09)60056-4

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (3): 599-608.doi: 10.1016/S0252-9602(09)60056-4

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

胡耀忠,龙红卫

Department of Mathematics, University of Kansas, 605 Snow Hall, Lawrence, Kansas 66045-2142, USA；Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA

收稿日期:2008-11-19 出版日期:2009-05-20 发布日期:2009-05-20
基金资助:
Hu is supported by the National Science Foundation under Grant No. DMS0504783; Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

Department of Mathematics, University of Kansas, 605 Snow Hall, Lawrence, Kansas 66045-2142, USA；Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA

Received:2008-11-19 Online:2009-05-20 Published:2009-05-20
Supported by:
Hu is supported by the National Science Foundation under Grant No. DMS0504783; Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science

摘要/Abstract

摘要：

We study the problem of parameter estimation for mean-reverting α-stable motion, dX_t = (α₀ − θ₀X_t)dt + dZ_t, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (α₀, θ₀) = (0, 0). If α₀ = 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.

关键词: asymptotic distribution of LSE, consistency of LSE, discrete observa-tion, least squares method, Ornstein-Uhlenbeck processes, mean-reverting processes, singularity, α-stable processes, stable stochastic integrals

Abstract:

Key words: asymptotic distribution of LSE, consistency of LSE, discrete observa-tion, least squares method, Ornstein-Uhlenbeck processes, mean-reverting processes, singularity, α-stable processes, stable stochastic integrals

中图分类号:

60G52

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(英文版), 2009, 29(3): 599-608.

HU Yao-Zhong, LONG Gong-Wei. ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS[J]. Acta mathematica scientia,Series B, 2009, 29(3): 599-608.

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ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

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