Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (2): 394-408.doi: 10.1016/S0252-9602(16)30008-X

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LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

Guangjun SHEN1, Xiuwei YIN1, Litan YAN2   

  1. 1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China;
    2. Department of Mathematics, Donghua University, Shanghai 201620, China
  • Received:2014-02-18 Revised:2015-04-28 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    Guangjun Shen was supported by the National Natural Science Foundation of China (11271020), the Distinguished Young Scholars Foundation of Anhui Province (1608085J06). Litan Yan was supported by the National Natural Science Foundation of China (11171062).

Abstract:

In this article, we study a least squares estimator (LSE) of θ for the Ornstein-Uhlenbeck process X0=0, dXt=θXtdt+dBta, b, t≥0 driven by weighted fractional Brownian motion Ba, b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s ∈[0, t]} as t tends to infinity.

Key words: Weighted fractional Brownian motion, least squares estimator, Ornstein-Uhl-enbeck process

CLC Number: 

  • 60G15
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