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On the estimation of parameters for linear stochastic differential equations
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  • Published: February 1999

On the estimation of parameters for linear stochastic differential equations

  • R. Khasminskii1,
  • N. Krylov2 &
  • N. Moshchuk3 

Probability Theory and Related Fields volume 113, pages 443–472 (1999)Cite this article

  • 175 Accesses

  • 7 Citations

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Abstract.

The estimation of arbitrary number of parameters in linear stochastic differential equation (SDE) is investigated. The local asymptotic normality (LAN) of families of distributions corresponding to this SDE is established and the asymptotic efficiency of the maximum likelihood estimator (MLE) is obtained for the wide class of loss functions with polynomial majorants. As an example a single-degree of freedom mechanical system is considered. The results generalize [8], where all elements of the drift matrix are estimated and the asymptotic efficiency is proved only for the bounded loss functions.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. e-mail: rafail@math.wayne.edu, , , , , , US

    R. Khasminskii

  2. Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. e-mail:krylov@math.umn.edu, , , , , , US

    N. Krylov

  3. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. e-mail:moshchuk@math.wayne.edu, , , , , , US

    N. Moshchuk

Authors
  1. R. Khasminskii
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  2. N. Krylov
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  3. N. Moshchuk
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Received: 12 March 1997 / Revised version: 22 June 1998

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Khasminskii, R., Krylov, N. & Moshchuk, N. On the estimation of parameters for linear stochastic differential equations. Probab. Theory Relat. Fields 113, 443–472 (1999). https://doi.org/10.1007/s004400050213

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  • Issue Date: February 1999

  • DOI: https://doi.org/10.1007/s004400050213

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  • Mathematics Subject Classification (1991): 62M, 62F
  • Key words: Linear stochastic differential equation – Local asymptotic normality – Maximum likelihood estimator – Asymptotic efficiency
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