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Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise

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Abstract

The statistical inference of the Vasicek model driven by small Lévy process has a long history. In this paper, we consider the problem of parameter estimation for Vasicek model dXt = (μ-θXt)dt + εdLdt, t ∈ [0,1], X0 = x0, driven by small fractional Levy noise with the known parameter d less than one half, based on discrete high-frequency observations at regularly spaced time points \(\{ {t_i} = \frac{i}{n},i = 1,2,...,n\} \). For the general case and the null recurrent case, the consistency as well as the asymptotic behavior of least squares estimation of unknown parameters μ and θ have been established as small dispersion coefficient ε → 0 and large sample size n → − simultaneously.

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Acknowledgments

The authors are very grateful to the anonymous referee and the editor for their insightful and valuable comments, which have improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, P. R. China

    Guang Jun Shen & Qing Bo Wang

  2. College of Mathematics and Computer Science, Tongling University, Tongling, 244000, P. R. China

    Xiu Wei Yin

Authors
  1. Guang Jun Shen
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  2. Qing Bo Wang
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  3. Xiu Wei Yin
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Corresponding author

Correspondence to Guang Jun Shen.

Additional information

Supported by the Distinguished Young Scholars Foundation of Anhui Province (Grant No. 1608085J06), Top Talent Project of University Discipline (speciality) (Grant No. gxbjZD03) and the National Natural Science Foundation of China (Grant No. 11901005)

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Shen, G.J., Wang, Q.B. & Yin, X.W. Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise. Acta. Math. Sin.-English Ser. 36, 443–461 (2020). https://doi.org/10.1007/s10114-020-9121-y

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  • DOI: https://doi.org/10.1007/s10114-020-9121-y

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