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Estimation of parameters of linear homogeneous stochastic differential equations

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  • Jankunas, Andrius
  • Khasminskii, Rafail Z.

Abstract

In this paper we investigate the problem of parametric estimation for multidimensional linear autonomous homogeneous stochastic differential equations. We prove the Local Asymptotical Normality (LAN) property, find the Maximum Likelihood Estimator (MLE), and prove an asymptotical efficiency of MLE for bounded loss functions, when the observation time tends to infinity.

Suggested Citation

  • Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:2:p:205-219
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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    Cited by:

    1. Dehay, D. & El Waled, K., 2013. "Nonparametric estimation problem for a time-periodic signal in a periodic noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 608-615.
    2. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Mishura, Yuliya, 2014. "Standard maximum likelihood drift parameter estimator in the homogeneous diffusion model is always strongly consistent," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 24-29.
    4. Loukianova, D. & Loukianov, O., 2005. "Uniform law of large numbers and consistency of estimators for Harris diffusions," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 347-355, October.
    5. Andrius Jankunas, 1999. "Local Asymptotic Normality for Linear Homogeneous Difference Equations with Non-Gaussian Noise," Journal of Theoretical Probability, Springer, vol. 12(3), pages 675-697, July.
    6. N. Lin & S. Lototsky, 2014. "Second-order continuous-time non-stationary Gaussian autoregression," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 19-49, April.

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