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On the estimation of parameters for linear stochastic differential equations |
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| Authors: | R. Khasminskii N. Krylov N. Moshchuk |
| Affiliation: | (1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. e-mail: rafail@math.wayne.edu, US;(2) Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. e-mail:krylov@math.umn.edu, US;(3) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. e-mail:moshchuk@math.wayne.edu, US |
| 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. Received: 12 March 1997 / Revised version: 22 June 1998 |
| Keywords: | Mathematics Subject Classification (1991): 62M 62F |
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