TY - JOUR

T1 - On the estimation of parameters for linear stochastic differential equations

AU - Khasminskii, R.

AU - Krylov, N.

AU - Moshchuk, N.

PY - 1999/3

Y1 - 1999/3

N2 - 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.

AB - 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.

KW - Asymptotic efficiency

KW - Linear stochastic differential equation

KW - Local asymptotic normality

KW - Maximum likelihood estimator

UR - http://www.scopus.com/inward/record.url?scp=0033434978&partnerID=8YFLogxK

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U2 - 10.1007/s004400050213

DO - 10.1007/s004400050213

M3 - Article

AN - SCOPUS:0033434978

VL - 113

SP - 443

EP - 472

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -