On the estimation of parameters for linear stochastic differential equations

R. Khasminskii, N. Krylov, N. Moshchuk

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish (US)
Pages (from-to)443-472
Number of pages30
JournalProbability Theory and Related Fields
Issue number3
StatePublished - Mar 1999


  • Asymptotic efficiency
  • Linear stochastic differential equation
  • Local asymptotic normality
  • Maximum likelihood estimator


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