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On the consistency of a least squares identification procedure. (English) Zbl 0657.93072
The paper considers the estimation of the parameter \(\alpha\) in the equation \[ dX_ t=f(\alpha)X_ tdt+U_ tdt+dW_ t. \] If \(\alpha^*_ T\) is the least squares estimate of \(\alpha\) based on \(\sigma \{X_ t,U_ t\); \(t\leq T\}\) then heuristically \(\alpha^*_ T\) is the minimizer of the quadratic function \[ \int^{T}_{0}(\dot X_ t-f(\alpha)X_ t-U_ t)'\Lambda (\dot X_ t-f(\alpha)X_ t-U_ t)dt \] for some nonnegative definite symmetric matrix \(\Lambda\). If \(\alpha_ 0\) is the true value of \(\alpha\) it is shown that \(\lim_{T\to \infty} \alpha^*_ T=\alpha_ 0\) under certain conditions.
Reviewer: R.Elliott

93E12 Identification in stochastic control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E10 Estimation and detection in stochastic control theory
93E03 Stochastic systems in control theory (general)
93C40 Adaptive control/observation systems
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