EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

doi:10.1016/S0252-9602(11)60365-2

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1851-1859.doi: 10.1016/S0252-9602(11)60365-2

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EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

HU Yao-Zhong, Nualart David, XIAO Wei-Lin^*, ZHANG Wei-Guo

Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, Kansas 66045-2142, USA； School of Business and Administration, South China University of Technology, Guangzhou 510641, China

Received:2010-03-27 Revised:2010-07-11 Online:2011-09-20 Published:2011-09-20
Contact: XIAO Wei-Lin,weilinhy@yahoo.com.cn E-mail:hu@math.ku.edu; nualart@math.ku.edu；weilinhy@yahoo.com.cn; wgzhang@scut.edu.cn
Supported by:
This work was supported by the National Science Foundations (DMS0504783; DMS0604207), National Science Fund for Distinguished Young Scholars of China (70825005).

Abstract

Abstract:

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess´een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

Key words: maximum likelihood estimator, fractional Brownian motions, strong consis-tency, central limit theorem, Berry-Ess´een bounds Stein’s method, Malli-avin calculus

CLC Number:

62G05

HU Yao-Zhong, Nualart David, XIAO Wei-Lin, ZHANG Wei-Guo. EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION[J].Acta mathematica scientia,Series B, 2011, 31(5): 1851-1859.

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EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

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